The displacement-time graphs of two moving particles make angles of 30$$^\circ$$ and 45$$^\circ$$ with the x-axis as shown in the figure. The ratio of their respective velocity is

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. The the ratio $${{{S_n}} \over {{S_{n + 1}}}}$$ 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/s²)

The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by :