$A$ body is projected vertically upward with a velocity of $20 \, m/s$ from the top of a tower of height $200 \, m$. With what velocity will it strike the ground (in $m/s$)? (Take $g = 10 \, m/s^2$)

If a body is thrown up with the velocity of $15 \, m/s$,then the maximum height attained by the body is .......... $m$ $(g = 10 \, m/s^2)$.

Two balls of the same size,but where the density of one is greater than that of the other,are dropped from the same height. Which ball will reach the Earth first (air resistance is negligible)?

$A$ bead is free to slide down a smooth wire tightly stretched between points $A$ and $B$ on a vertical circle. If the bead starts from rest at $A$,the highest point on the circle,

$A$ tennis ball is released from a height $h$ and after freely falling on a wooden floor,it rebounds and reaches a height $\frac{h}{2}$. The velocity versus height of the ball during its motion may be represented graphically by (graphs are drawn schematically and not to scale):

$A$ 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