Application of Projectile to a Height

Q. A stone is projected from a point on the ground in such a direction as to hit a bird on the top of a telegraph post of height $h$ and then attain the maximum height $3h/2$ above the ground. If at the instant of projection, the bird were to fly away horizontally with uniform speed, find the ratio between the horizontal velocities of the bird and the stone if the stone still hits the bird while descending. Take $\sqrt{3}=1.73$.

Q. A body is thrown horizontally from the top of a tower of height 5 m. It touches the ground at a distance of 10 m from the foot of the tower. The initial velocity of the body is (g = 10 $m{s}^{-2}$)

1. $2.5m{s}^{-1}$
2. $5m{s}^{-1}$
3. $10m{s}^{-1}$
4. $20m{s}^{-1}$

Q.

A gun is aimed at a target in a line of its barrel. The target is released and allowed to fall under gravity at the same instant the gun is fired. The bullet will

1. Pass above the target

2. Pass below the target

3. Hit the target

4. Certainly miss the target

Q.

At the height 80 m, an aeroplane is moving with 150 m/s. A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped (given g = 10 $m/s^2$)

1. 605.3 m

2. 600 m

3. 80 m

4. 230 m

Q.

A gun is aimed at a target in a line of its barrel. The target is released and allowed to fall under gravity at the same instant the gun is fired. The bullet will

1. Pass above the target

2. Pass below the target

3. Hit the target

4. Certainly miss the target