B M Sharma Solutions for Chapter: Kinematics I, Exercise 54: CONCEPT APPLICATION EXERCISE 4.4

A moving sidewalk in an airport terminal building moves at a speed of $1.0 \mathrm{m} {\mathrm{s}}^{-1}$ and is $35.0 \mathrm{m}$ long. If a woman steps on at one end and walks at$1.5 \mathrm{m} {\mathrm{s}}^{-1}$ relative to the moving side walk, then find the time that she requires to reach the opposite end,

(a) when she walks in the same direction the side walk is moving and

(b) when she walks in the opposite direction.

A lift is moving up with acceleration $a$. A person inside the lift throws the ball upwards with a velocity $u$ relative to hand.

(a) What is the time of flight of the ball?

(b)  What is the maximum height reached by the ball in the lift? 

Two cars ${\mathrm{C}}_1 \mathrm{and} {\mathrm{C}}_2$ and moving in the same direction on a straight single lane road with velocities $12 \mathrm{m} {\mathrm{s}}^{-1}$ and $10 \mathrm{m} {\mathrm{s}}^{-1}$ respectively. When the separation between the two cars was $d=200 \mathrm{m}$, ${\mathrm{C}}_2$ started accelerating to avoid collision. What is the minimum acceleration of car ${\mathrm{C}}_2$ (in $\mathrm{cm} {\mathrm{s}}^{-2}$) so that they do not collide?

Two boys enter a running escalator at the ground floor in a shopping mall and they do some fun on it. The first boy repeatedly follows $p_1=1$ step up and then $q_1=2$ steps down whereas the second boy repeatedly follows $p_2=2$ steps up and then $q_1=1$ step down. Both of them move relative to the escalator with speed $v_r=50 \mathrm{cm} {\mathrm{s}}^{-1}$. If the first boy takes $t_1=250 \mathrm{s}$ and the second boy takes $t_2=50 \mathrm{s}$ to reach the first floor, how fast is the escalator running?

The speed of a motor launch with respect to water in a stream is $8 \mathrm{m} {\mathrm{s}}^{-1}$, while water current's speed is $3 \mathrm{m} {\mathrm{s}}^{-1}$. When the launch began travelling upstream, a float was dropped from it. After travelling a distance of $4.8 \mathrm{km}$ upstream, the launch turned back and caught up with the float. What is the total time which elapsed during the process?

Two boats $A$ and $B$ moved away from a buoy anchored in the middle of a river. $A$ moved along the river and $B$ at right angle to it. Having moved off equal distances from the buoy, the boats returned. Find the ratio of the times of motion of the boats, if the velocity of each boat with respect to still water is $\eta$ times greater than the velocity of water current.

A ship of length $l=150 \mathrm{m}$ moving with velocity $v_s=36 \mathrm{km} {\mathrm{h}}^{-1}$ on the sea, suddenly discovered straight ahead a sinking boat people having met an accident. A rescue boat has been lowered from the mid of the ship, which went to the sinking boat with speed $v_b=72 \mathrm{km} {\mathrm{h}}^{-1}$. When the rescue boat overtakes the leading edge of the ship, the sinking boat was $x_0=3.0 \mathrm{km}$ away. The rescue boat reaches the sinking boat, spends $t_0=1.0 \min$ to take the people on board, and then returned with the same speed to the mid of the ship where it was lowered. Determine the time taken in the whole rescue operation from the moment the rescue boat was lowered to the moment the rescue boat returned to the ship.

 A $10 \mathrm{km}$ long straight road connects two towns $A$ and $B$. Two cyclists simultaneously start one from town $A$ and the other from town $B$. On reaching the opposite town, a cyclist immediately returns to his starting town whereas the other cyclist takes some rest and then returns to his starting town. Both of them can ride at speed $20 \mathrm{km} {\mathrm{h}}^{-1}$ in absence of wind but during their whole journey uniform wind from town $A$ to $B$ increases the speed of the cyclist going into the wind by the same amount as it decreases the speed of the cyclist going against the wind. Both the cyclists meet twice, first at $2 \mathrm{km}$ and then $6 \mathrm{km}$ away from one of the towns. For what period does a cyclist rest?