Curves:- Helix & Spirals
Q.1 An inelastic string of 100 mm length is wound round a cylinder of 50 mm diameter keeping the string always tight. Draw the curve generated by end point of the string. Name the Curve.
Q.2 A point P is moving around the surface of a cone of base 80 mm & height 90 mm. If the point P starting from the apex, reaches the periphery of cone base, in one and half turns. Draw the projection of the path of P. Assume that the axial descent of the point in uniform with its rotation.
Q.3 A right Angle triangle of two sides 33 mm and 53 mm & hypotenuse 62.5 mm is rotating around side of 53 mm. A point P is moving up on the hypotenuse. During the rotation of the triangle point P moves from the bottom most position to highest position on hypotenuse while the triangle completes one revolution. Both the movements are uniform. Draw the path of the point P in elevation & Plan. Name the curve of plan & curve of elevation.
Q.4 Draw one convolutions of the Archimedean spiral represented by the polar equation
r = 32 + 7 * θ , where r is in mm and θ is in radian. Draw the tangent and normal to the curve at point 55 mm from the pole.
Q.5 A pendulum oscillates in a plane through an angle of 200 on either side of the plumb line & makes one oscillation .During this period , an ant moves on the pendulum from bottom end to top with uniform velocity. Trace the path of the ant.
Q.6 A straight line AB of 60 mm length rotates clockwise about its end A for one complete revolution & during this period, a point P moves along the straight line from A to B & returns back to the point A .if the rotary motion of the straight line about point A & linear motion of point P along AB are both uniform, draw the path of the point P . Name the curve. Draw Normal & Tangent to the curve at a point 35 mm from the point A.
Q.7 Draw a triangle AOB with OA=30 mm, OB=50 mm & AOB =120 0. Draw an Archimedean spiral passing through points A & B with O as a pole. Complete the curve starting from O. Also draw tangent & normal to the curve at a distance of 27 mm from O. (Refer Jolhe PN 6.37)
Wednesday, September 23, 2009
Curves:- Helix & Spirals
Q.1 An inelastic string of 100 mm length is wound round a cylinder of 50 mm diameter keeping the string always tight. Draw the curve generated by end point of the string. Name the Curve.
Q.2 A point P is moving around the surface of a cone of base 80 mm & height 90 mm. If the point P starting from the apex, reaches the periphery of cone base, in one and half turns. Draw the projection of the path of P. Assume that the axial descent of the point in uniform with its rotation.
Q.3 A right Angle triangle of two sides 33 mm and 53 mm & hypotenuse 62.5 mm is rotating around side of 53 mm. A point P is moving up on the hypotenuse. During the rotation of the triangle point P moves from the bottom most position to highest position on hypotenuse while the triangle completes one revolution. Both the movements are uniform. Draw the path of the point P in elevation & Plan. Name the curve of plan & curve of elevation.
Q.4 Draw one convolutions of the Archimedean spiral represented by the polar equation
r = 32 + 7 * θ , where r is in mm and θ is in radian. Draw the tangent and normal to the curve at point 55 mm from the pole.
Q.5 A pendulum oscillates in a plane through an angle of 200 on either side of the plumb line & makes one oscillation .During this period , an ant moves on the pendulum from bottom end to top with uniform velocity. Trace the path of the ant.
Q.6 A straight line AB of 60 mm length rotates clockwise about its end A for one complete revolution & during this period, a point P moves along the straight line from A to B & returns back to the point A .if the rotary motion of the straight line about point A & linear motion of point P along AB are both uniform, draw the path of the point P . Name the curve. Draw Normal & Tangent to the curve at a point 35 mm from the point A.
Q.7 Draw a triangle AOB with OA=30 mm, OB=50 mm & AOB =120 0. Draw an Archimedean spiral passing through points A & B with O as a pole. Complete the curve starting from O. Also draw tangent & normal to the curve at a distance of 27 mm from O. (Refer Jolhe PN 6.37)
Q.1 An inelastic string of 100 mm length is wound round a cylinder of 50 mm diameter keeping the string always tight. Draw the curve generated by end point of the string. Name the Curve.
Q.2 A point P is moving around the surface of a cone of base 80 mm & height 90 mm. If the point P starting from the apex, reaches the periphery of cone base, in one and half turns. Draw the projection of the path of P. Assume that the axial descent of the point in uniform with its rotation.
Q.3 A right Angle triangle of two sides 33 mm and 53 mm & hypotenuse 62.5 mm is rotating around side of 53 mm. A point P is moving up on the hypotenuse. During the rotation of the triangle point P moves from the bottom most position to highest position on hypotenuse while the triangle completes one revolution. Both the movements are uniform. Draw the path of the point P in elevation & Plan. Name the curve of plan & curve of elevation.
Q.4 Draw one convolutions of the Archimedean spiral represented by the polar equation
r = 32 + 7 * θ , where r is in mm and θ is in radian. Draw the tangent and normal to the curve at point 55 mm from the pole.
Q.5 A pendulum oscillates in a plane through an angle of 200 on either side of the plumb line & makes one oscillation .During this period , an ant moves on the pendulum from bottom end to top with uniform velocity. Trace the path of the ant.
Q.6 A straight line AB of 60 mm length rotates clockwise about its end A for one complete revolution & during this period, a point P moves along the straight line from A to B & returns back to the point A .if the rotary motion of the straight line about point A & linear motion of point P along AB are both uniform, draw the path of the point P . Name the curve. Draw Normal & Tangent to the curve at a point 35 mm from the point A.
Q.7 Draw a triangle AOB with OA=30 mm, OB=50 mm & AOB =120 0. Draw an Archimedean spiral passing through points A & B with O as a pole. Complete the curve starting from O. Also draw tangent & normal to the curve at a distance of 27 mm from O. (Refer Jolhe PN 6.37)
Curves:- Cycloid
Q.1 A circle of 50 mm diameter rolls on a horizontal line for a half revolution & then on a vertical line for another half revolution. Draw the curve traced out by a point P on the circumference of the circle . Name the curve . Draw tangent and normal at a point 25 mm away from the horizontal line.
Q.2 ABC is an equilateral triangle of side equal to 70 mm.Trace the locus of the vertices A & B when the circle circumscribing ABC rolls without slipping along a fixed straight line for 2/3 rd revolution.
Q.3 Draw an equilateral triangle ABC of side 70 mm. trace the path of point B when the circle circumscribing the triangle rolls on a straight line which is tangent to circle at point A without slipping for one complete revolution.
Q.4 A circle is rolling on line on OA generates the cycloid. Line OB is inclined at 300 to A .Line OB is tangent to the cycloid at B. Find the diameters of the circle & reproduce the cycloid to which OB is tangent at B . Also find initial position of centre of circle with respect to O. Take OB= 60 mm.
Q.5 A vertical line AB 50 mm long is a diameter of a circle .The circle rolls without slipping on a horizontal line AC. Draw the path traced out by circle. Name the curve.
Q.6 A car is going up a hill. If the road is inclined at 15 0 to the horizontal. Draw the locus of a point on the wheel tyre of diameter 550 mm.
Q.7 A circular base of 30 mm diameter rolls on another fixed disc of 60 mm diameter. With external contact, for one complete revolution of the rolling circle . Draw the curve traced out by appoint P, on the rim of the rolling disc, which is situated diametrically opposite to the point of contact in the starting position.Also draw the curve traced by the point of contact. Q of the two circular discs in the initial position.
Q.8 Prove that the hypocycloid is a straight line if the diameter of generating circle is equal to the radius of the directing circle. (Draw a hypocycloid when the radius of the directing circle R = 60 mm and the radius of the rolling circle r = 30 mm).
Q.9 A circle of Ф 40 mm rolls without slipping on the inside of another circle of Ф 160 mm. Draw the path traced by a point P on the circumference of the rolling circle , diametrically opposite to the initial point of contact between circles, when the rolling circle makes one rotation clockwise . Also draw the locus traced by the initial point of contact Q of the circles.
Q.1 A circle of 50 mm diameter rolls on a horizontal line for a half revolution & then on a vertical line for another half revolution. Draw the curve traced out by a point P on the circumference of the circle . Name the curve . Draw tangent and normal at a point 25 mm away from the horizontal line.
Q.2 ABC is an equilateral triangle of side equal to 70 mm.Trace the locus of the vertices A & B when the circle circumscribing ABC rolls without slipping along a fixed straight line for 2/3 rd revolution.
Q.3 Draw an equilateral triangle ABC of side 70 mm. trace the path of point B when the circle circumscribing the triangle rolls on a straight line which is tangent to circle at point A without slipping for one complete revolution.
Q.4 A circle is rolling on line on OA generates the cycloid. Line OB is inclined at 300 to A .Line OB is tangent to the cycloid at B. Find the diameters of the circle & reproduce the cycloid to which OB is tangent at B . Also find initial position of centre of circle with respect to O. Take OB= 60 mm.
Q.5 A vertical line AB 50 mm long is a diameter of a circle .The circle rolls without slipping on a horizontal line AC. Draw the path traced out by circle. Name the curve.
Q.6 A car is going up a hill. If the road is inclined at 15 0 to the horizontal. Draw the locus of a point on the wheel tyre of diameter 550 mm.
Q.7 A circular base of 30 mm diameter rolls on another fixed disc of 60 mm diameter. With external contact, for one complete revolution of the rolling circle . Draw the curve traced out by appoint P, on the rim of the rolling disc, which is situated diametrically opposite to the point of contact in the starting position.Also draw the curve traced by the point of contact. Q of the two circular discs in the initial position.
Q.8 Prove that the hypocycloid is a straight line if the diameter of generating circle is equal to the radius of the directing circle. (Draw a hypocycloid when the radius of the directing circle R = 60 mm and the radius of the rolling circle r = 30 mm).
Q.9 A circle of Ф 40 mm rolls without slipping on the inside of another circle of Ф 160 mm. Draw the path traced by a point P on the circumference of the rolling circle , diametrically opposite to the initial point of contact between circles, when the rolling circle makes one rotation clockwise . Also draw the locus traced by the initial point of contact Q of the circles.
Curves:- Cycloid
Q.1 A circle of 50 mm diameter rolls on a horizontal line for a half revolution & then on a vertical line for another half revolution. Draw the curve traced out by a point P on the circumference of the circle . Name the curve . Draw tangent and normal at a point 25 mm away from the horizontal line.
Q.2 ABC is an equilateral triangle of side equal to 70 mm.Trace the locus of the vertices A & B when the circle circumscribing ABC rolls without slipping along a fixed straight line for 2/3 rd revolution.
Q.3 Draw an equilateral triangle ABC of side 70 mm. trace the path of point B when the circle circumscribing the triangle rolls on a straight line which is tangent to circle at point A without slipping for one complete revolution.
Q.4 A circle is rolling on line on OA generates the cycloid. Line OB is inclined at 300 to A .Line OB is tangent to the cycloid at B. Find the diameters of the circle & reproduce the cycloid to which OB is tangent at B . Also find initial position of centre of circle with respect to O. Take OB= 60 mm.
Q.5 A vertical line AB 50 mm long is a diameter of a circle .The circle rolls without slipping on a horizontal line AC. Draw the path traced out by circle. Name the curve.
Q.6 A car is going up a hill. If the road is inclined at 15 0 to the horizontal. Draw the locus of a point on the wheel tyre of diameter 550 mm.
Q.7 A circular base of 30 mm diameter rolls on another fixed disc of 60 mm diameter. With external contact, for one complete revolution of the rolling circle . Draw the curve traced out by appoint P, on the rim of the rolling disc, which is situated diametrically opposite to the point of contact in the starting position.Also draw the curve traced by the point of contact. Q of the two circular discs in the initial position.
Q.8 Prove that the hypocycloid is a straight line if the diameter of generating circle is equal to the radius of the directing circle. (Draw a hypocycloid when the radius of the directing circle R = 60 mm and the radius of the rolling circle r = 30 mm).
Q.9 A circle of Ф 40 mm rolls without slipping on the inside of another circle of Ф 160 mm. Draw the path traced by a point P on the circumference of the rolling circle , diametrically opposite to the initial point of contact between circles, when the rolling circle makes one rotation clockwise . Also draw the locus traced by the initial point of contact Q of the circles.
Q.2 ABC is an equilateral triangle of side equal to 70 mm.Trace the locus of the vertices A & B when the circle circumscribing ABC rolls without slipping along a fixed straight line for 2/3 rd revolution.
Q.3 Draw an equilateral triangle ABC of side 70 mm. trace the path of point B when the circle circumscribing the triangle rolls on a straight line which is tangent to circle at point A without slipping for one complete revolution.
Q.4 A circle is rolling on line on OA generates the cycloid. Line OB is inclined at 300 to A .Line OB is tangent to the cycloid at B. Find the diameters of the circle & reproduce the cycloid to which OB is tangent at B . Also find initial position of centre of circle with respect to O. Take OB= 60 mm.
Q.5 A vertical line AB 50 mm long is a diameter of a circle .The circle rolls without slipping on a horizontal line AC. Draw the path traced out by circle. Name the curve.
Q.6 A car is going up a hill. If the road is inclined at 15 0 to the horizontal. Draw the locus of a point on the wheel tyre of diameter 550 mm.
Q.7 A circular base of 30 mm diameter rolls on another fixed disc of 60 mm diameter. With external contact, for one complete revolution of the rolling circle . Draw the curve traced out by appoint P, on the rim of the rolling disc, which is situated diametrically opposite to the point of contact in the starting position.Also draw the curve traced by the point of contact. Q of the two circular discs in the initial position.
Q.8 Prove that the hypocycloid is a straight line if the diameter of generating circle is equal to the radius of the directing circle. (Draw a hypocycloid when the radius of the directing circle R = 60 mm and the radius of the rolling circle r = 30 mm).
Q.9 A circle of Ф 40 mm rolls without slipping on the inside of another circle of Ф 160 mm. Draw the path traced by a point P on the circumference of the rolling circle , diametrically opposite to the initial point of contact between circles, when the rolling circle makes one rotation clockwise . Also draw the locus traced by the initial point of contact Q of the circles.
Curves:- Involute
Q.1 A thread of 130 mm length is wound round a solid section of a regular hexagon of 20 mm side, keeping one end of the thread firmly attached to a corner of the hexagon. It is unwound in an anticlockwise direction, keeping the unwinding end tight. Draw the path traced by the unwinding end of the thread & Name the curve.
Q.2 A line PQ =120 mm long rolls without slipping on the periphery of a semicircle of diameter AB = 70 mm as shown in figure 1. Initially the line is tangent to the circle at A such that AP=100 mm. Draw the loci pf ends of the line. Name the curve.
Q.3 Draw the path of the end of thread 140 mm long, when it is wound on a half hexagon of sides 25 mm.
Q.4 Take length PQ=50 mm. Draw a semicircle considering this as diameter. On the other side of the semicircle, construct a half of a regular hexagon of 25 mm side. Let R and S be the remaining two corners of the half hexagon PSRQ, an inelastic string 150 mm long is attached to corner R . Draw the curve traced out by the free end of the string, when it is completely wound around the figure 2. Keeping the string always tight & in clockwise direction. Name the curve.
Q.5 A Semicircle with O as centre & 60 mm diameter is fixed as shown in figure 3. PQ is an inelastic string of 130 mm length end P of the string is fixed & is 20 mm above the centre O. the string is rotated in clockwise direction, Draw the locus of the Point Q.
Q.6 A disc in the form of a semicircle & a semi triangular hexagon of thickness 10 mm is shown in figure 4 . A disc is firmly fixed at point O. An inelastic string of length 160 mm is fixed at point A & the free end B of the string is wound round the disc in anticlockwise direction. Draw the locus of B.
Q.7 A pole Shown in figure 5 is to be wrapped by means of thread AB, by keeping the thread always tight. Draw the locus of point B if the end A is fixed at position.
Q.8 A disc is in the form of a square of 30 mm side surrounded by a semicircle on one side & a half hexagon on the opposite side as shown in figure 6 . Draw the path of the end of string unwound from the circumference of the disc. Name the curve.
Q.1 A thread of 130 mm length is wound round a solid section of a regular hexagon of 20 mm side, keeping one end of the thread firmly attached to a corner of the hexagon. It is unwound in an anticlockwise direction, keeping the unwinding end tight. Draw the path traced by the unwinding end of the thread & Name the curve.
Q.2 A line PQ =120 mm long rolls without slipping on the periphery of a semicircle of diameter AB = 70 mm as shown in figure 1. Initially the line is tangent to the circle at A such that AP=100 mm. Draw the loci pf ends of the line. Name the curve.
Q.3 Draw the path of the end of thread 140 mm long, when it is wound on a half hexagon of sides 25 mm.
Q.4 Take length PQ=50 mm. Draw a semicircle considering this as diameter. On the other side of the semicircle, construct a half of a regular hexagon of 25 mm side. Let R and S be the remaining two corners of the half hexagon PSRQ, an inelastic string 150 mm long is attached to corner R . Draw the curve traced out by the free end of the string, when it is completely wound around the figure 2. Keeping the string always tight & in clockwise direction. Name the curve.
Q.5 A Semicircle with O as centre & 60 mm diameter is fixed as shown in figure 3. PQ is an inelastic string of 130 mm length end P of the string is fixed & is 20 mm above the centre O. the string is rotated in clockwise direction, Draw the locus of the Point Q.
Q.6 A disc in the form of a semicircle & a semi triangular hexagon of thickness 10 mm is shown in figure 4 . A disc is firmly fixed at point O. An inelastic string of length 160 mm is fixed at point A & the free end B of the string is wound round the disc in anticlockwise direction. Draw the locus of B.
Q.7 A pole Shown in figure 5 is to be wrapped by means of thread AB, by keeping the thread always tight. Draw the locus of point B if the end A is fixed at position.
Q.8 A disc is in the form of a square of 30 mm side surrounded by a semicircle on one side & a half hexagon on the opposite side as shown in figure 6 . Draw the path of the end of string unwound from the circumference of the disc. Name the curve.
Assignment 1 (C)
Subject: ENGINEERING GRAPHICS -I
Class F.E Division :- C
Topic :- Hyperbola
Select a suitable scale
Faculty:- Prof. D.B.Shelke
Q.1 For a perfect gas , the relation between the pressure P & Volume V in isothermal (constant temperature) expansion is given by PV = Constant. Draw the curve of isothermal expansion of an enclosed volume of gas if 3 m3 of the gas correspond to a pressure of 4 KN/m2 . Draw the graph P Vs V for pressure range 1 KN/m2 to 10 KN/m2. Determine graphically
(i) The Volume of gas at a pressure corresponding to 3 KN/m2.
(ii) The pressure corresponding to volume of 4.5 m3
Q.2 0.025 m3 of air at a pressure of 6 Kgf/cm2 absolute expands until its volume is 0.25 m3 .The relation between the pressure & volume is given by the formula PV=0.15. Construct the expansion curve .Choose pressure scale 1 cm = 0.5 Kgf/cm2 & Volume scale 1 cm = 0.05 m3 . Name the curve.
Q.3 Draw the locus of a particle moving in such a way that the product of its distance from two fixed lines, at right angles to each other is constant, if a point on the curve is 20 mm & 45 mm from lines. Name the curve and draw normal & tangent at any point to the curve.
Q.4 Two straight lines OA & OB make an angle of 75 0 between them, P is a point 40 mm from OA & 50 mm from OB. Draw hyperbola through P with OA & OB as asymptote . Determine its eccentricity & show the focus.
Q.5 A perfect gas follows the law PV=Constant .At a pressure 3 Kgf/cm2 absolute, the volume of gas being 2 m3. Draw the graph P Vs V for pressure range 1 Kgf/cm2 absolute to 10 Kgf/cm2 absolute .Name the curve.
Q.6 The asymptote of a hyperbola are inclined at 70 0 to each other . A point P on the curve is 20 mm & 26 mm from the asymptotes. Construct the curve showing at least 3 points on either side of P . Determine the eccentricity of the curve.
Q.7 Two points A & B are located on a plane sheet of paper and are 80 mm apart. A point P moves on the sheet such that difference of its distances from A & B always remains 40 mm. Draw locus of point P & also draw its directrix and asymptotes.
Q.8 The asymptotes of a hyperbola are at right angle to each other & a point P on the curve is at a distance of 25 mm from the asymptote .Draw the two branches of the hyperbola.
Subject: ENGINEERING GRAPHICS -I
Class F.E Division :- C
Topic :- Hyperbola
Select a suitable scale
Faculty:- Prof. D.B.Shelke
Q.1 For a perfect gas , the relation between the pressure P & Volume V in isothermal (constant temperature) expansion is given by PV = Constant. Draw the curve of isothermal expansion of an enclosed volume of gas if 3 m3 of the gas correspond to a pressure of 4 KN/m2 . Draw the graph P Vs V for pressure range 1 KN/m2 to 10 KN/m2. Determine graphically
(i) The Volume of gas at a pressure corresponding to 3 KN/m2.
(ii) The pressure corresponding to volume of 4.5 m3
Q.2 0.025 m3 of air at a pressure of 6 Kgf/cm2 absolute expands until its volume is 0.25 m3 .The relation between the pressure & volume is given by the formula PV=0.15. Construct the expansion curve .Choose pressure scale 1 cm = 0.5 Kgf/cm2 & Volume scale 1 cm = 0.05 m3 . Name the curve.
Q.3 Draw the locus of a particle moving in such a way that the product of its distance from two fixed lines, at right angles to each other is constant, if a point on the curve is 20 mm & 45 mm from lines. Name the curve and draw normal & tangent at any point to the curve.
Q.4 Two straight lines OA & OB make an angle of 75 0 between them, P is a point 40 mm from OA & 50 mm from OB. Draw hyperbola through P with OA & OB as asymptote . Determine its eccentricity & show the focus.
Q.5 A perfect gas follows the law PV=Constant .At a pressure 3 Kgf/cm2 absolute, the volume of gas being 2 m3. Draw the graph P Vs V for pressure range 1 Kgf/cm2 absolute to 10 Kgf/cm2 absolute .Name the curve.
Q.6 The asymptote of a hyperbola are inclined at 70 0 to each other . A point P on the curve is 20 mm & 26 mm from the asymptotes. Construct the curve showing at least 3 points on either side of P . Determine the eccentricity of the curve.
Q.7 Two points A & B are located on a plane sheet of paper and are 80 mm apart. A point P moves on the sheet such that difference of its distances from A & B always remains 40 mm. Draw locus of point P & also draw its directrix and asymptotes.
Q.8 The asymptotes of a hyperbola are at right angle to each other & a point P on the curve is at a distance of 25 mm from the asymptote .Draw the two branches of the hyperbola.
Assignment 1 (B)
Subject : Engineering Graphics I
Unit II : Curves used in Engineering Practices
Topic : Methods of Construction of parabola Date of Submission : 1St Oct.2009
Class : F.E.
Division : C Name of the Faculty : Prof. D.B.Shelke
Instructions : Do not rub off construction lines.
Construction work should be very thin.
Write procedure to every method of construction.
Q.1 Draw the locus of a point which is equidistant from a point & a Line which is 5 cm away from the given fixed point. Name the curve and draw tangent and normal at any point on the curve.
Q.2 On a cricket ground, the ball thrown by a fielder reaches the wicket keeper following parabolic path, max height achieved by the ball above the ground is 30 m . Assuming the point of throw & the point of catch to be 1 m above the ground. Draw the path of the ball the distance between the fielder and the wicket keeper is 70 m.
Q.3 Two lines OA & OB are at right angles to each other OA is 140 mm long & horizontal whereas OB is 100 mm long & is vertical. Construct a parabola to pass through A & B.
Q.4 Draw a parabola circumscribing an isosceles triangle of base 80 mm & altitudes 50 mm.
Q.5 Construct a ▲ABC of sides AB= 80 mm , BC = 60 mm & AC = 50 mm. Draw parabola passing through all the vertices of triangle.
Q.6 AOB is a right angled triangle with OA=OB=45 mm & AOB = 900 .Draw a parabola passing through points A & B.
Q.7 An Artillery gun fires a bombshell from ground surface to a target on the same level & 15 Km away. Bomb shell achieves a maximum height 5 Km. Draw path traced by shell selecting a suitable scale. Also draw normal and tangent to the curve at any point on the curve and show Focus and directrix.
Q.8 Draw a parabola whose double ordinate is 120 mm and the angle of projection is 55 0 .Find its focus & directrix . Also draw a pair of tangents from a convenient point P outside the curve.
Subject : Engineering Graphics I
Unit II : Curves used in Engineering Practices
Topic : Methods of Construction of parabola Date of Submission : 1St Oct.2009
Class : F.E.
Division : C Name of the Faculty : Prof. D.B.Shelke
Instructions : Do not rub off construction lines.
Construction work should be very thin.
Write procedure to every method of construction.
Q.1 Draw the locus of a point which is equidistant from a point & a Line which is 5 cm away from the given fixed point. Name the curve and draw tangent and normal at any point on the curve.
Q.2 On a cricket ground, the ball thrown by a fielder reaches the wicket keeper following parabolic path, max height achieved by the ball above the ground is 30 m . Assuming the point of throw & the point of catch to be 1 m above the ground. Draw the path of the ball the distance between the fielder and the wicket keeper is 70 m.
Q.3 Two lines OA & OB are at right angles to each other OA is 140 mm long & horizontal whereas OB is 100 mm long & is vertical. Construct a parabola to pass through A & B.
Q.4 Draw a parabola circumscribing an isosceles triangle of base 80 mm & altitudes 50 mm.
Q.5 Construct a ▲ABC of sides AB= 80 mm , BC = 60 mm & AC = 50 mm. Draw parabola passing through all the vertices of triangle.
Q.6 AOB is a right angled triangle with OA=OB=45 mm & AOB = 900 .Draw a parabola passing through points A & B.
Q.7 An Artillery gun fires a bombshell from ground surface to a target on the same level & 15 Km away. Bomb shell achieves a maximum height 5 Km. Draw path traced by shell selecting a suitable scale. Also draw normal and tangent to the curve at any point on the curve and show Focus and directrix.
Q.8 Draw a parabola whose double ordinate is 120 mm and the angle of projection is 55 0 .Find its focus & directrix . Also draw a pair of tangents from a convenient point P outside the curve.
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