A balloon starts rising upwards with constant acceleration $a$ and after time $t_0$ second, a packet is dropped from it which reaches the ground after $t$ seconds of dropping. Determine the value of$t .$

(a) Show that the velocity acquired by a particle in sliding down an inclined plane is the same as that acquired by a particle falling freely from rest through a distance equal to the height of the inclined plane.

(b) Find the time taken in sliding a particle down the whole length of the incline.

Ball $1$ is released from the top of a smooth inclined plane, and at the same instant ball $2$ is projected from the foot of the plane with such a velocity that they meet halfway up the incline. Determine:

(a) the velocity with which balls are projected and

(b) the velocity of each ball when they meet.

Mark the following statements as true or false. 

(a) (i) A ball thrown vertically up takes more time to go up than to come down. 

(ii) If a ball starts falling from the position of rest, then it travels a distance of $25 \mathrm{m}$ during the third second of its fall

(iii) A packet dropped from a rising balloon first moves upwards and then moves downward as observed by a stationary observer on the ground.

(iv) In the absence of air resistance, all bodies fall on the surface of earth at the same rate.

A ball thrown up from the ground reaches a maximum height of 20 m. Find:

(a) Its initial velocity.

(b) The time taken to reach the highest point.

(c)  Its velocity just before hitting the ground. 

(d) Its displacement between $0.5 \mathrm{s}$ and $2.5 \mathrm{s}$.

(e) The time at which it is $15 \mathrm{m}$ above the ground.

A ball is dropped from an elevator at an altitude of $200 \mathrm{m}$. How much time will the ball take to reach the ground if the elevator is

(a) Stationary?

(b) Ascending with velocity $10{ \mathrm{m} \mathrm{s}}^{-1}$?

(c) Descending with velocity $10{ \mathrm{m} \mathrm{s}}^{-1}$?