$A$ ball is dropped from a bridge that is $45 \ m$ above the water. It falls directly into a boat which is moving with constant velocity. The boat is $12 \ m$ away from the point of impact when the ball is dropped. The speed of the boat is (Take $g=10 \ m \ s^{-2}$) (in $m \ s^{-1}$)

$A$ ball is thrown up vertically with a certain velocity so that it reaches a maximum height $h$. Find the ratio of the times at which it is at height $\frac{h}{3}$ while going up and coming down respectively.

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 $g = 10 \,m \,s^{-2}$]

$A$ stone is shot straight upward with a speed of $20\, m/s$ from a tower $200\, m$ high. The speed with which it strikes the ground is approximately........$m/s$.

$A$ boy throws balls into the air at a regular interval of $2 \, s$. The next ball is thrown when the velocity of the first ball is zero. How high does the ball rise above his hand (in $, m$)? [Take $g = 9.8 \, m/s^2$]

$A$ particle is released from rest from a tower of height $3h$. The ratio of times taken to fall through successive equal heights $h$,i.e.,$t_1 : t_2 : t_3$ is