EXERCISES

A ball A is dropped from the top of a building and at the same time an identical ball B is thrown vertically upwards from the ground. When the balls collide the speed of A is twice that of B. At what fraction of the height of the building did the collision occur?

Drops of water fall at the regular intervals from the roof of a building of height $16 \mathrm{m}$. The first drop strikes the ground at the same moment as the fifth drop leaves the roof. Find the distances between successive drops.

A hunter aims a gun at a monkey hanging from a tree some distance away. The monkey drops from the branch at the moment he fires the gun hoping to avoid the bullet. Explain why the monkey made a wrong move.

A food packet is dropped from an aeroplane, moving with a speed of $360 \mathrm{kmph}$ in a horizontal direction from a height of $500 \mathrm{m}$. Find its time of descent in seconds. ($g=10 \mathrm{m}/{\mathrm{s}}^2$)

A food packet is dropped from an aeroplane, moving with a speed of $360 \mathrm{kmph}$ in a horizontal direction, from a height of $500 \mathrm{m}$. Find the horizontal distance between the point at which the food packet reaches the ground and the point above which it was dropped. $(g=10 \mathrm{m}/{\mathrm{s}}^2)$

A ball is tossed from the window of a building with an initial velocity of $8 {\mathrm{ms}}^{-1}$ at an angle of $20°$ below the horizontal. It strikes the ground $3 \mathrm{s}$ later. From what height was the ball thrown? How far from the base of the building does the ball strike the ground? ($g=9.8 \mathrm{m}/{\mathrm{s}}^2, \cos 20°=0.94, \sin 20°=0.34$)

Two balls are projected from the same point in the directions $30°$ and $60°$ with respect to the horizontal. What is the ratio of their initial velocities if they attain the same height?

Two balls are projected from the same point in the directions $30°$ and $60°$ with respect to the horizontal. What is the ratio of their initial velocities if they have the same range?