Uniformly accelerated motion relations

A bullet from a gun is fired on a rectangular wooden block with velocity \(u\). When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes \(\frac{u}{3}\). Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is :

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity \(4\,\mathrm{m\,s^{-1}}\). The ball strikes the water surface after 4 s. The height of bridge above water surface is (Take \(g=10\,\mathrm{m\,s^{-2}}\)) :

The ratio of the distances travelled by a freely falling body in the \(1^{st}\), \(2^{nd}\), \(3^{rd}\) and \(4^{th}\) second :

A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let \(S_n\) be the distance travelled by the block in the interval t = n − 1 to t = n. Then, the ratio \(\frac{S_n}{S_{n+1}}\) is :

A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is : (g = 10 m/s\(^2\))

When an object is shot from the bottom of a long smooth inclined plane kept at an angle \(60^\circ\) with horizontal, it can travel a distance \(x_1\) along the plane. But when the inclination is decreased to \(30^\circ\) and the same object is shot with the same velocity, it can travel \(x_2\) distance. Then \(x_1 : x_2\) will be :