Consider two cases, in case (a) a ball that has been thrown straight upward from the edge of a cliff. The initial speed of the ball is $20 \mathrm{m} {\mathrm{s}}^{-1}$. It goes up and then falls back down, eventually hitting the ground beneath the cliff. In case (b) the ball has been thrown straight downward at the same initial speed. In the absence of air resistance, would the ball in case (b) strike the ground with (i) smaller speed than in case (a), (ii) same speed as in case (a), or (iii) greater speed than the ball in case (a)?

 

A cricket match customarily begins with a coin toss. The umpire tosses the coin up with an initial speed of $5.0 \mathrm{m} {\mathrm{s}}^{-1}$. In the absence of air resistance,

(a) how high does the coin go above its point of release?
(b) what is the total time the coin is in the air before returning to its release point?

A ball is projected vertically up such that it passes through a fixed point after a time $t_1$ and $t_2$, respectively. Find

(a) the height at which the point is located with respect to the point of projection.
(b) the speed of projection of the ball.
(c) the velocity of the ball at the time of passing through point $P$.

(d) (i) the maximum height reached by the ball relative to the point of projection $A$, and
(ii) maximum height reached by the ball relative to point $P$ under consideration.

(e) the average speed and average velocity of the ball during the motion from $A$ to $P$ for the time $t_1$ and $t_2$, respectively.

Two particles $1$ and $2$ are projected simultaneously with velocities $v_1$ and $v_2$, respectively. Particle $1$ is projected vertically up from the top of a cliff of height $h$ and particle$2$ is projected vertically up from the bottom of the cliff. If the bodies meet

(a) above the top of the cliff,

(b) between the top and bottom of the cliff, and

(c) below the bottom of the cliff, find the time of meeting of the particles.

A body is thrown vertically upwards from $A$, the top of a tower. It reaches the ground in time $t_1.$ If it is thrown vertically downwards from $A$ with the same speed it reaches the ground in time $t_2.$ If it is allowed to fall freely from $A$, then find the time it takes to reach the ground.

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$t .$