B M Sharma Solutions for Chapter: Kinematics I, Exercise 36: CONCEPT APPLICATION EXERCISE 4.3

A balloon rises from rest on the ground with constant acceleration $\frac{g}{8}$. A stone is dropped from the balloon when the balloon has risen to a height of $H$. Find the time taken by the stone to reach the ground. 

A parachutist, after bailing out, falls $50 \mathrm{m}$ without friction. When the parachute opens, it decelerates at $2 \mathrm{m} {\mathrm{s}}^{-2}$. He reaches the ground with a speed of $3 \mathrm{m} {\mathrm{s}}^{-1}$. At what height did he bailout? 

A ball is dropped from the top of a tower of height $h$. It covers a distance of $\frac{h}{2}$ in the last second of its motion. How long does the ball remain in the air? 

You are on the roof of the physics building, $46.0 \mathrm{m}$ above the ground. Your physics professor, who is $1.80 \mathrm{m}$ tall, is walking alongside the building at a constant speed of $1.20 \mathrm{m} {\mathrm{s}}^{-1}$. If you wish to drop a flower on your professor's head, where should the professor be when you release the flower? Assume that the flower is in free fall. (Take g = $9.8 \mathrm{m} {\mathrm{s}}^{-2}$)
 

Two particles are simultaneously released from points $A$ and $D$ as shown in figure. How should the value of $H$ be adjusted in order that the two particles collide? Neglect dissipative forces.

 A ball is thrown from the top of a tower in vertically upward direction. Velocity at a point $h \mathrm{m}$ below the point of projection is twice of the velocity at a point $h \mathrm{m}$ above the point of projection. Find the maximum height reached by the ball above the top of tower.
 

A ball is thrown upward from the ground with an initial speed of $25 \mathrm{m} {\mathrm{s}}^{-1}$ at the same instant, another ball is dropped from a building $15 \mathrm{m}$ high. After how long will the balls be at the same height above the ground? 

At time $t=0$, a student throws a set of keys vertically upward to her sorority sister, who is in a window at distance $h$ above. The second student catches the keys at time $t$.

(a) With what initial velocity was the keys thrown?

(b) What was the velocity of the keys just before they were caught?