From the top of a tower,a particle is thrown vertically downwards with a velocity of $10\; m/s$. The ratio of the distances covered by it in the $3^{rd}$ and $2^{nd}$ seconds of the motion is (Take $g = 10\; m/s^2$).

$A$ stone falls freely under gravity. It covers distances $d_1$ and $d_2$ in the first $4$ seconds and the next $8$ seconds, respectively. The ratio $\frac{d_2}{d_1}$ is

$A$ 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 .......... $m$ :-

$A$ stone thrown upward with a speed $u$ from the top of a tower reaches the ground with a velocity $3u$. The height of the tower is (in $u^2/g$)

$A$ 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 $m \ s^{-1}$)

Two balls $A$ and $B$ are thrown with the same velocity $u$ from the top of a tower. Ball $A$ is thrown vertically upwards and ball $B$ is thrown vertically downwards. If $t_A = 6 \ s$ and $t_B = 2 \ s$,then the height of the tower is ......... $m$.