OBLIQUE PROJECTILE
Motion in Plane

269961 A particle is fired with velocity u making angle \(\theta\) with the horizontal. What is the change in velocity when it is at the highest point ?

1 \(u \cos \theta\)
2 u
3 \(u \sin \theta\)
4 \((u \cos \theta-u)\)
Motion in Plane

269962 Two projectiles \(A\) and \(B\) are thrown from the same point with velocities \(v\) and \(\frac{v}{2}\) respectively. If \(B\) is thrown at an angle \(45^{\circ}\) with horizontal. What is the inclination of \(A\). when their ranges are the same?

1 \(\sin ^{-1} \square \frac{1}{-1} \square\)
2 \(\frac{1}{2} \sin ^{-1} \square^{-1} \theta\)
3 \(2 \sin ^{-1} \square^{1}-4\)
4 \(\frac{1}{2} \sin ^{-1} \square \frac{1}{9} \theta\)
Motion in Plane

269963 A particle is projected with a velocity \(v\) such that its range on the horizontal plane is twice the greatest height attained by it, The range of the projectile is (when it is acceleration due to gravity is ' \(g\) ') [PMT 2010]

1 \(\frac{4 v^{2}}{5 g}\)
2 \(\frac{4 g}{5 v^{2}}\)
3 \(\frac{v^{2}}{g}\)
4 \(\frac{4 v^{2}}{\sqrt{5 g}}\)
Motion in Plane

269964 A number of bullets are fired in all possible directions with the same initial velocity \(u\). The maximum area of ground covered by bullets is

1 \(\pi \stackrel{\square u^{2} \square^{2}}{\square} \frac{\square}{\square}\)
2 \(\pi \stackrel{\square u^{2}}{\square 2 g} \square\)
3 \(\pi \stackrel{\square u \overbrace{\square}}{\square g}\)
4 \(\pi \frac{\square u}{\square \square^{2 g}} \bar{b}_{0}^{2}\)
Motion in Plane

269965 A ball is projected from the ground with a velocity 'u' such that its range is maximum. Then

1 Its velocity at half the maximum height is \(\frac{\sqrt{3}}{2} u\)
2 Its velocity at the maximum height is ' \(u\) '.
3 Change in its velocity when it returns to the ground is 'u'.
4 all the above are true.
Motion in Plane

269961 A particle is fired with velocity u making angle \(\theta\) with the horizontal. What is the change in velocity when it is at the highest point ?

1 \(u \cos \theta\)
2 u
3 \(u \sin \theta\)
4 \((u \cos \theta-u)\)
Motion in Plane

269962 Two projectiles \(A\) and \(B\) are thrown from the same point with velocities \(v\) and \(\frac{v}{2}\) respectively. If \(B\) is thrown at an angle \(45^{\circ}\) with horizontal. What is the inclination of \(A\). when their ranges are the same?

1 \(\sin ^{-1} \square \frac{1}{-1} \square\)
2 \(\frac{1}{2} \sin ^{-1} \square^{-1} \theta\)
3 \(2 \sin ^{-1} \square^{1}-4\)
4 \(\frac{1}{2} \sin ^{-1} \square \frac{1}{9} \theta\)
Motion in Plane

269963 A particle is projected with a velocity \(v\) such that its range on the horizontal plane is twice the greatest height attained by it, The range of the projectile is (when it is acceleration due to gravity is ' \(g\) ') [PMT 2010]

1 \(\frac{4 v^{2}}{5 g}\)
2 \(\frac{4 g}{5 v^{2}}\)
3 \(\frac{v^{2}}{g}\)
4 \(\frac{4 v^{2}}{\sqrt{5 g}}\)
Motion in Plane

269964 A number of bullets are fired in all possible directions with the same initial velocity \(u\). The maximum area of ground covered by bullets is

1 \(\pi \stackrel{\square u^{2} \square^{2}}{\square} \frac{\square}{\square}\)
2 \(\pi \stackrel{\square u^{2}}{\square 2 g} \square\)
3 \(\pi \stackrel{\square u \overbrace{\square}}{\square g}\)
4 \(\pi \frac{\square u}{\square \square^{2 g}} \bar{b}_{0}^{2}\)
Motion in Plane

269965 A ball is projected from the ground with a velocity 'u' such that its range is maximum. Then

1 Its velocity at half the maximum height is \(\frac{\sqrt{3}}{2} u\)
2 Its velocity at the maximum height is ' \(u\) '.
3 Change in its velocity when it returns to the ground is 'u'.
4 all the above are true.
Motion in Plane

269961 A particle is fired with velocity u making angle \(\theta\) with the horizontal. What is the change in velocity when it is at the highest point ?

1 \(u \cos \theta\)
2 u
3 \(u \sin \theta\)
4 \((u \cos \theta-u)\)
Motion in Plane

269962 Two projectiles \(A\) and \(B\) are thrown from the same point with velocities \(v\) and \(\frac{v}{2}\) respectively. If \(B\) is thrown at an angle \(45^{\circ}\) with horizontal. What is the inclination of \(A\). when their ranges are the same?

1 \(\sin ^{-1} \square \frac{1}{-1} \square\)
2 \(\frac{1}{2} \sin ^{-1} \square^{-1} \theta\)
3 \(2 \sin ^{-1} \square^{1}-4\)
4 \(\frac{1}{2} \sin ^{-1} \square \frac{1}{9} \theta\)
Motion in Plane

269963 A particle is projected with a velocity \(v\) such that its range on the horizontal plane is twice the greatest height attained by it, The range of the projectile is (when it is acceleration due to gravity is ' \(g\) ') [PMT 2010]

1 \(\frac{4 v^{2}}{5 g}\)
2 \(\frac{4 g}{5 v^{2}}\)
3 \(\frac{v^{2}}{g}\)
4 \(\frac{4 v^{2}}{\sqrt{5 g}}\)
Motion in Plane

269964 A number of bullets are fired in all possible directions with the same initial velocity \(u\). The maximum area of ground covered by bullets is

1 \(\pi \stackrel{\square u^{2} \square^{2}}{\square} \frac{\square}{\square}\)
2 \(\pi \stackrel{\square u^{2}}{\square 2 g} \square\)
3 \(\pi \stackrel{\square u \overbrace{\square}}{\square g}\)
4 \(\pi \frac{\square u}{\square \square^{2 g}} \bar{b}_{0}^{2}\)
Motion in Plane

269965 A ball is projected from the ground with a velocity 'u' such that its range is maximum. Then

1 Its velocity at half the maximum height is \(\frac{\sqrt{3}}{2} u\)
2 Its velocity at the maximum height is ' \(u\) '.
3 Change in its velocity when it returns to the ground is 'u'.
4 all the above are true.
Motion in Plane

269961 A particle is fired with velocity u making angle \(\theta\) with the horizontal. What is the change in velocity when it is at the highest point ?

1 \(u \cos \theta\)
2 u
3 \(u \sin \theta\)
4 \((u \cos \theta-u)\)
Motion in Plane

269962 Two projectiles \(A\) and \(B\) are thrown from the same point with velocities \(v\) and \(\frac{v}{2}\) respectively. If \(B\) is thrown at an angle \(45^{\circ}\) with horizontal. What is the inclination of \(A\). when their ranges are the same?

1 \(\sin ^{-1} \square \frac{1}{-1} \square\)
2 \(\frac{1}{2} \sin ^{-1} \square^{-1} \theta\)
3 \(2 \sin ^{-1} \square^{1}-4\)
4 \(\frac{1}{2} \sin ^{-1} \square \frac{1}{9} \theta\)
Motion in Plane

269963 A particle is projected with a velocity \(v\) such that its range on the horizontal plane is twice the greatest height attained by it, The range of the projectile is (when it is acceleration due to gravity is ' \(g\) ') [PMT 2010]

1 \(\frac{4 v^{2}}{5 g}\)
2 \(\frac{4 g}{5 v^{2}}\)
3 \(\frac{v^{2}}{g}\)
4 \(\frac{4 v^{2}}{\sqrt{5 g}}\)
Motion in Plane

269964 A number of bullets are fired in all possible directions with the same initial velocity \(u\). The maximum area of ground covered by bullets is

1 \(\pi \stackrel{\square u^{2} \square^{2}}{\square} \frac{\square}{\square}\)
2 \(\pi \stackrel{\square u^{2}}{\square 2 g} \square\)
3 \(\pi \stackrel{\square u \overbrace{\square}}{\square g}\)
4 \(\pi \frac{\square u}{\square \square^{2 g}} \bar{b}_{0}^{2}\)
Motion in Plane

269965 A ball is projected from the ground with a velocity 'u' such that its range is maximum. Then

1 Its velocity at half the maximum height is \(\frac{\sqrt{3}}{2} u\)
2 Its velocity at the maximum height is ' \(u\) '.
3 Change in its velocity when it returns to the ground is 'u'.
4 all the above are true.
Motion in Plane

269961 A particle is fired with velocity u making angle \(\theta\) with the horizontal. What is the change in velocity when it is at the highest point ?

1 \(u \cos \theta\)
2 u
3 \(u \sin \theta\)
4 \((u \cos \theta-u)\)
Motion in Plane

269962 Two projectiles \(A\) and \(B\) are thrown from the same point with velocities \(v\) and \(\frac{v}{2}\) respectively. If \(B\) is thrown at an angle \(45^{\circ}\) with horizontal. What is the inclination of \(A\). when their ranges are the same?

1 \(\sin ^{-1} \square \frac{1}{-1} \square\)
2 \(\frac{1}{2} \sin ^{-1} \square^{-1} \theta\)
3 \(2 \sin ^{-1} \square^{1}-4\)
4 \(\frac{1}{2} \sin ^{-1} \square \frac{1}{9} \theta\)
Motion in Plane

269963 A particle is projected with a velocity \(v\) such that its range on the horizontal plane is twice the greatest height attained by it, The range of the projectile is (when it is acceleration due to gravity is ' \(g\) ') [PMT 2010]

1 \(\frac{4 v^{2}}{5 g}\)
2 \(\frac{4 g}{5 v^{2}}\)
3 \(\frac{v^{2}}{g}\)
4 \(\frac{4 v^{2}}{\sqrt{5 g}}\)
Motion in Plane

269964 A number of bullets are fired in all possible directions with the same initial velocity \(u\). The maximum area of ground covered by bullets is

1 \(\pi \stackrel{\square u^{2} \square^{2}}{\square} \frac{\square}{\square}\)
2 \(\pi \stackrel{\square u^{2}}{\square 2 g} \square\)
3 \(\pi \stackrel{\square u \overbrace{\square}}{\square g}\)
4 \(\pi \frac{\square u}{\square \square^{2 g}} \bar{b}_{0}^{2}\)
Motion in Plane

269965 A ball is projected from the ground with a velocity 'u' such that its range is maximum. Then

1 Its velocity at half the maximum height is \(\frac{\sqrt{3}}{2} u\)
2 Its velocity at the maximum height is ' \(u\) '.
3 Change in its velocity when it returns to the ground is 'u'.
4 all the above are true.