03. Projectile Motion
Motion in Plane

143779 Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is \(\pi / 3\) and the maximum height reached by it is \(102 \mathrm{~m}\). Then the maximum height reached by the other in \(\mathrm{m}\) is :

1 336
2 224
3 56
4 34
Motion in Plane

143780 A projectile has initially the same horizontal velocity as it would acquire, if it had moved from rest with uniform acceleration of \(3 \mathrm{~ms}^{-2}\) for 0.5 minute. If the maximum height reached by it is \(80 \mathrm{~m}\), then the angle of projection is: \((\mathrm{g}=\) \(10 \mathrm{~ms}^{-2}\) )

1 \(\tan ^{-1}(3)\)
2 \(\tan ^{-1}\left(\frac{3}{2}\right)\)
3 \(\tan ^{-1}\left(\frac{4}{9}\right)\)
4 \(\sin ^{-1}\left(\frac{4}{9}\right)\)
Motion in Plane

143781 It is possible to project a particle with a given speed in two possible ways so that, it has the same horizontal range \(R\). The product of the times taken by it in two possible ways is :
[g= acceleration due to gravity]

1 \(\frac{R}{g}\)
2 \(\frac{2 R}{g}\)
3 \(\frac{3 R}{g}\)
4 \(\frac{4 R}{g}\)
Motion in Plane

143782 A stone is projected with a velocity \(u\) at angle \(\theta\) with the horizontal reaches maximum height \(H_{1}\), when it is projected with a velocity \(u\) at an angle \(\left(\frac{\pi}{2}-\theta\right)\) with the horizontal, it reaches to a maximum height \(\mathrm{H}_{2}\). The relation between the horizontal range \(r\) of the projectile, \(H_{1}\) and \(\mathrm{H}_{2}\) is:

1 \(\mathrm{R}=4 \sqrt{\mathrm{H}_{1} \mathrm{H}_{2}}\)
2 \(\mathrm{R}=4\left(\mathrm{H}_{1}-\mathrm{H}_{2}\right)\)
3 \(\mathrm{R}=4\left(\mathrm{H}_{1}+\mathrm{H}_{2}\right)\)
4 \(\mathrm{R}=\mathrm{H}_{1}^{2} / \mathrm{H}_{2}^{2}\)
Motion in Plane

143783 For a projectile the ratio of maximum height reached to the square of flight time is:
\(\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)\)

1 \(5: 4\)
2 \(5: 2\)
3 \(5: 1\)
4 \(10: 1\)
Motion in Plane

143779 Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is \(\pi / 3\) and the maximum height reached by it is \(102 \mathrm{~m}\). Then the maximum height reached by the other in \(\mathrm{m}\) is :

1 336
2 224
3 56
4 34
Motion in Plane

143780 A projectile has initially the same horizontal velocity as it would acquire, if it had moved from rest with uniform acceleration of \(3 \mathrm{~ms}^{-2}\) for 0.5 minute. If the maximum height reached by it is \(80 \mathrm{~m}\), then the angle of projection is: \((\mathrm{g}=\) \(10 \mathrm{~ms}^{-2}\) )

1 \(\tan ^{-1}(3)\)
2 \(\tan ^{-1}\left(\frac{3}{2}\right)\)
3 \(\tan ^{-1}\left(\frac{4}{9}\right)\)
4 \(\sin ^{-1}\left(\frac{4}{9}\right)\)
Motion in Plane

143781 It is possible to project a particle with a given speed in two possible ways so that, it has the same horizontal range \(R\). The product of the times taken by it in two possible ways is :
[g= acceleration due to gravity]

1 \(\frac{R}{g}\)
2 \(\frac{2 R}{g}\)
3 \(\frac{3 R}{g}\)
4 \(\frac{4 R}{g}\)
Motion in Plane

143782 A stone is projected with a velocity \(u\) at angle \(\theta\) with the horizontal reaches maximum height \(H_{1}\), when it is projected with a velocity \(u\) at an angle \(\left(\frac{\pi}{2}-\theta\right)\) with the horizontal, it reaches to a maximum height \(\mathrm{H}_{2}\). The relation between the horizontal range \(r\) of the projectile, \(H_{1}\) and \(\mathrm{H}_{2}\) is:

1 \(\mathrm{R}=4 \sqrt{\mathrm{H}_{1} \mathrm{H}_{2}}\)
2 \(\mathrm{R}=4\left(\mathrm{H}_{1}-\mathrm{H}_{2}\right)\)
3 \(\mathrm{R}=4\left(\mathrm{H}_{1}+\mathrm{H}_{2}\right)\)
4 \(\mathrm{R}=\mathrm{H}_{1}^{2} / \mathrm{H}_{2}^{2}\)
Motion in Plane

143783 For a projectile the ratio of maximum height reached to the square of flight time is:
\(\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)\)

1 \(5: 4\)
2 \(5: 2\)
3 \(5: 1\)
4 \(10: 1\)
Motion in Plane

143779 Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is \(\pi / 3\) and the maximum height reached by it is \(102 \mathrm{~m}\). Then the maximum height reached by the other in \(\mathrm{m}\) is :

1 336
2 224
3 56
4 34
Motion in Plane

143780 A projectile has initially the same horizontal velocity as it would acquire, if it had moved from rest with uniform acceleration of \(3 \mathrm{~ms}^{-2}\) for 0.5 minute. If the maximum height reached by it is \(80 \mathrm{~m}\), then the angle of projection is: \((\mathrm{g}=\) \(10 \mathrm{~ms}^{-2}\) )

1 \(\tan ^{-1}(3)\)
2 \(\tan ^{-1}\left(\frac{3}{2}\right)\)
3 \(\tan ^{-1}\left(\frac{4}{9}\right)\)
4 \(\sin ^{-1}\left(\frac{4}{9}\right)\)
Motion in Plane

143781 It is possible to project a particle with a given speed in two possible ways so that, it has the same horizontal range \(R\). The product of the times taken by it in two possible ways is :
[g= acceleration due to gravity]

1 \(\frac{R}{g}\)
2 \(\frac{2 R}{g}\)
3 \(\frac{3 R}{g}\)
4 \(\frac{4 R}{g}\)
Motion in Plane

143782 A stone is projected with a velocity \(u\) at angle \(\theta\) with the horizontal reaches maximum height \(H_{1}\), when it is projected with a velocity \(u\) at an angle \(\left(\frac{\pi}{2}-\theta\right)\) with the horizontal, it reaches to a maximum height \(\mathrm{H}_{2}\). The relation between the horizontal range \(r\) of the projectile, \(H_{1}\) and \(\mathrm{H}_{2}\) is:

1 \(\mathrm{R}=4 \sqrt{\mathrm{H}_{1} \mathrm{H}_{2}}\)
2 \(\mathrm{R}=4\left(\mathrm{H}_{1}-\mathrm{H}_{2}\right)\)
3 \(\mathrm{R}=4\left(\mathrm{H}_{1}+\mathrm{H}_{2}\right)\)
4 \(\mathrm{R}=\mathrm{H}_{1}^{2} / \mathrm{H}_{2}^{2}\)
Motion in Plane

143783 For a projectile the ratio of maximum height reached to the square of flight time is:
\(\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)\)

1 \(5: 4\)
2 \(5: 2\)
3 \(5: 1\)
4 \(10: 1\)
Motion in Plane

143779 Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is \(\pi / 3\) and the maximum height reached by it is \(102 \mathrm{~m}\). Then the maximum height reached by the other in \(\mathrm{m}\) is :

1 336
2 224
3 56
4 34
Motion in Plane

143780 A projectile has initially the same horizontal velocity as it would acquire, if it had moved from rest with uniform acceleration of \(3 \mathrm{~ms}^{-2}\) for 0.5 minute. If the maximum height reached by it is \(80 \mathrm{~m}\), then the angle of projection is: \((\mathrm{g}=\) \(10 \mathrm{~ms}^{-2}\) )

1 \(\tan ^{-1}(3)\)
2 \(\tan ^{-1}\left(\frac{3}{2}\right)\)
3 \(\tan ^{-1}\left(\frac{4}{9}\right)\)
4 \(\sin ^{-1}\left(\frac{4}{9}\right)\)
Motion in Plane

143781 It is possible to project a particle with a given speed in two possible ways so that, it has the same horizontal range \(R\). The product of the times taken by it in two possible ways is :
[g= acceleration due to gravity]

1 \(\frac{R}{g}\)
2 \(\frac{2 R}{g}\)
3 \(\frac{3 R}{g}\)
4 \(\frac{4 R}{g}\)
Motion in Plane

143782 A stone is projected with a velocity \(u\) at angle \(\theta\) with the horizontal reaches maximum height \(H_{1}\), when it is projected with a velocity \(u\) at an angle \(\left(\frac{\pi}{2}-\theta\right)\) with the horizontal, it reaches to a maximum height \(\mathrm{H}_{2}\). The relation between the horizontal range \(r\) of the projectile, \(H_{1}\) and \(\mathrm{H}_{2}\) is:

1 \(\mathrm{R}=4 \sqrt{\mathrm{H}_{1} \mathrm{H}_{2}}\)
2 \(\mathrm{R}=4\left(\mathrm{H}_{1}-\mathrm{H}_{2}\right)\)
3 \(\mathrm{R}=4\left(\mathrm{H}_{1}+\mathrm{H}_{2}\right)\)
4 \(\mathrm{R}=\mathrm{H}_{1}^{2} / \mathrm{H}_{2}^{2}\)
Motion in Plane

143783 For a projectile the ratio of maximum height reached to the square of flight time is:
\(\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)\)

1 \(5: 4\)
2 \(5: 2\)
3 \(5: 1\)
4 \(10: 1\)
Motion in Plane

143779 Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is \(\pi / 3\) and the maximum height reached by it is \(102 \mathrm{~m}\). Then the maximum height reached by the other in \(\mathrm{m}\) is :

1 336
2 224
3 56
4 34
Motion in Plane

143780 A projectile has initially the same horizontal velocity as it would acquire, if it had moved from rest with uniform acceleration of \(3 \mathrm{~ms}^{-2}\) for 0.5 minute. If the maximum height reached by it is \(80 \mathrm{~m}\), then the angle of projection is: \((\mathrm{g}=\) \(10 \mathrm{~ms}^{-2}\) )

1 \(\tan ^{-1}(3)\)
2 \(\tan ^{-1}\left(\frac{3}{2}\right)\)
3 \(\tan ^{-1}\left(\frac{4}{9}\right)\)
4 \(\sin ^{-1}\left(\frac{4}{9}\right)\)
Motion in Plane

143781 It is possible to project a particle with a given speed in two possible ways so that, it has the same horizontal range \(R\). The product of the times taken by it in two possible ways is :
[g= acceleration due to gravity]

1 \(\frac{R}{g}\)
2 \(\frac{2 R}{g}\)
3 \(\frac{3 R}{g}\)
4 \(\frac{4 R}{g}\)
Motion in Plane

143782 A stone is projected with a velocity \(u\) at angle \(\theta\) with the horizontal reaches maximum height \(H_{1}\), when it is projected with a velocity \(u\) at an angle \(\left(\frac{\pi}{2}-\theta\right)\) with the horizontal, it reaches to a maximum height \(\mathrm{H}_{2}\). The relation between the horizontal range \(r\) of the projectile, \(H_{1}\) and \(\mathrm{H}_{2}\) is:

1 \(\mathrm{R}=4 \sqrt{\mathrm{H}_{1} \mathrm{H}_{2}}\)
2 \(\mathrm{R}=4\left(\mathrm{H}_{1}-\mathrm{H}_{2}\right)\)
3 \(\mathrm{R}=4\left(\mathrm{H}_{1}+\mathrm{H}_{2}\right)\)
4 \(\mathrm{R}=\mathrm{H}_{1}^{2} / \mathrm{H}_{2}^{2}\)
Motion in Plane

143783 For a projectile the ratio of maximum height reached to the square of flight time is:
\(\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)\)

1 \(5: 4\)
2 \(5: 2\)
3 \(5: 1\)
4 \(10: 1\)