An iron block is dropped into a deep well. The sound of the splash is heard after $4.23 \, s$. If the depth of the well is $78.4 \, m$,find the speed of sound in air in $m/s$ $\left(g = 9.8 \, m/s^2\right)$.

Two stones are thrown up simultaneously from the edge of a cliff $200 \; m$ high with initial speeds of $15 \; m s^{-1}$ and $30 \; m s^{-1}$. Verify that the graph shown in Figure correctly represents the time variation of the relative position of the second stone with respect to the first. Neglect air resistance and assume that the stones do not rebound after hitting the ground. Take $g = 10 \; m s^{-2}$. Give the equations for the linear and curved parts of the plot.

$A$ body,thrown upwards with some velocity,reaches a maximum height of $50 \,m$. Another body with double the mass,thrown up with double the initial velocity,will reach a maximum height of............$m$.

$A$ 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 $12 \; s$.

$A$ body is dropped from a height $h$. If it acquires a momentum $p$ just before striking the ground,then the mass of the body is

$A$ packet is dropped from a balloon which is going upwards with a velocity of $12 \, m/s$. The velocity of the packet after $2 \, s$ will be ........ $m/s$.