Two balls $A$ and $B$ are placed at the top of a $180 \,m$ tall tower. Ball $A$ is released from the top at $t = 0 \,s$. Ball $B$ is thrown vertically downward with an initial velocity $u$ at $t = 2 \,s$. Both balls meet at a point $100 \,m$ above the ground. Find the value of $u$ in $m \,s^{-1}$. [Use $g = 10 \,m \,s^{-2}$]

Balls are thrown vertically upward in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is $5 \ m$,the number of balls thrown per minute will be

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.

Two spherical balls having equal masses with a radius of $5 \, \text{cm}$ each are thrown upwards along the same vertical direction at an interval of $3 \, \text{s}$ with the same initial velocity of $35 \, \text{m/s}$. These balls collide at a height of $\ldots \ldots \ldots \, \text{m}$. (Take $g = 10 \, \text{m/s}^2$)

The velocity-time curve for a body projected vertically upwards is:

$A$ stone is thrown upwards with a velocity $50 \,ms^{-1}$. Another stone is simultaneously thrown downwards from the same location with a velocity $50 \,ms^{-1}$. When the first stone is at the highest point, the velocity of the second stone is $...... \,ms^{-1}$ (Take $g = 10 \,ms^{-2}$).