$A$ parachutist,after bailing out,falls $20\,m$ without friction. When the parachute opens,it decelerates at $2\,m/s^2$. He reaches the ground with a speed of $4\,m/s$. At what height did he bail out (in $,m$)?

$A$ man in a balloon rising vertically with an acceleration of $4.9\,m/s^2$ releases a ball $2\,s$ after the balloon is let go from the ground. The greatest height above the ground reached by the ball is...........$m$ $(g = 9.8\,m/s^2)$

The ratio of the displacements of a freely falling body during the second and fifth seconds of its motion is

$A$ juggler tosses a ball up in the air with initial speed $u$. At the instant it reaches its maximum height $H$,he tosses up a second ball with the same initial speed. The two balls will collide at a height:

An object of mass $5 \, kg$ is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of $10 \, N$ throughout the motion. The ratio of time of ascent to the time of descent will be equal to [Use $g = 10 \, ms^{-2}$]

$A$ ball is dropped from a height of $90 \; m$ on a floor. At each collision with the floor,the ball loses one-tenth of its speed. Plot the speed-time graph of its motion between $t = 0$ to $12 \; s$.