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Motion on an Inclined Plane

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2021 1 question

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:

2019 1 question

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 the shot with the same velocity, it can travel $x_2$ distance. Then $x_1:x_2$ will be: