Two bodies of masses $m_1$ and $m_2$ are dropped from two different heights $h_1$ and $h_2$ respectively. The ratio of the times taken by the two masses to touch the ground is (neglect air resistance)

$A$ body is falling freely from a point $A$ at a certain height from the ground and passes through points $B, C$, and $D$ (vertically as shown below) such that $BC = CD$. The time taken by the particle to move from $B$ to $C$ is $2 \ s$ and from $C$ to $D$ is $1 \ s$. The time taken to move from $A$ to $B$ in seconds is

$A$ body dropped from a height $h$ with an initial speed zero,strikes the ground with a velocity $3 \ km/h$. Another body of the same mass is dropped from the same height $h$ with an initial speed of $4 \ km/h$. Find the final velocity of the second body with which it strikes the ground in $km/h$.

$A$ juggler tosses a ball up in the air with initial speed $u$. At the instant it reaches its maximum height $H$,he tosses up a second ball with the same initial speed. The two balls will collide at a height:

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.

$A$ particle is thrown with any velocity vertically upward. The distance travelled by the particle in the first second of its descent is: