Free Fall

A ball is dropped from a high rise platform at, $t=0$ starting from rest. After $6 \mathrm{s}$ another ball is thrown downwards from the same platform with the speed $v$. The two balls meet at, $t=18 \mathrm{s}$. What is the value of $v$? (Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ )

Two bodies, $\mathrm{A}$ (of mass $1 \mathrm{kg}$) and $\mathrm{B}$ (of mass $3 \mathrm{kg}$), are dropped from heights of $16 \mathrm{m}$ and $25 \mathrm{m}$, respectively. The ratio of the times taken by them to reach the ground is

The water drops fall at regular intervals from a tap $5\hspace{0.17em}\mathrm{m}$ above the ground. The third drop is leaving the tap at an instant when the first drop touches the ground. How far above the ground is the second drop at that instant?  (Take $g=10\hspace{0.17em}\mathrm{m} {\mathrm{s}}^{-\mathrm{2}}$)

A stone released with zero velocity from the top of a tower, reaches the ground in $4$ sec. The height of the tower is  $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

A body is thrown vertically upward from the ground. It reaches a maximum height of $20 \mathrm{m}$ in $5 \sec$. After what time, it will reach the ground from its maximum height position?

A body falling freely from a given height $\text{'}H\text{'}$ hits an inclined plane in its path at a height $\text{'}h\text{'}$. As a result of this impact, the direction of the velocity of the body becomes horizontal. For what value of $\left(\frac{h}{H}\right)$ the body will take maximum time to reach the ground?

A ball is released from the top of a tower of height $h$ metres. It takes $T$ seconds to reach the ground. What is the position of the ball in $\frac{T}{3}$ seconds?

From a building two balls A and B are thrown such that A is thrown upwards and B downwards (both vertically with same speed). If  $v_A$ and  $v_B$ are their respective velocities on reaching the ground, then –

If a body is released from certain height then final velocity become

A $0.4 \mathrm{kg}$ mass takes $8 \mathrm{s}$ to reach ground when dropped from a certain height 'P' above surface of earth. The loss of potential energy in the last second of fall is _____ $\mathrm{J}$. [Take $g=10 {\mathrm{ms}}^{-2}$]

A particle is thrown vertically upward with initial velocity of $150 \mathrm{m} {\mathrm{s}}^{-1}$. Find the ratio of its speed at $t = 3 \mathrm{s}$ and $t = 5 \mathrm{s}$. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A body is projected from ground, vertically upwards travels a distance h in the last second of its total journey. If it is projected with twice the previous velocity, the distance travelled in last second of its journey, is 

A stone starts falling freely under gravity. The time taken by the stone to fall through the initial height $h$ is $4 \mathrm{s}$. The further time taken to fall through the next $2h$ height will be closest to

A particle is thrown vertically upwards from the surface of the earth. Let $T_P$ be the time taken by the particle to travel from a point $P$ above the earth to its highest point and back to the point $P$. Similarly, let $T_Q$ be the time taken by the particle to travel from another point $Q$ above the earth to its highest point and back to the same point $Q$. If the distance between the points $P$ and $Q$ is $H$, find the expression for acceleration due to gravity in terms of $T_P$, $T_Q$ and $H$.

A helicopter ascending at the rate of $12 \mathrm{m} {\mathrm{s}}^{-1}$ drops a food packet from a height of $80 \mathrm{m}$ above the ground. The time the packet takes to reach the ground is