Q9 of 28 Page 55

Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km/h in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road?

Given,


Speed of the cyclist, v = 20 km/h = 5.55 m/s


Time period for same direction bus pass by cyclist= 18 min = 1080 s


Time period for opposite direction bus pass by cyclist=6 min = 360 s


Let, The velocity if the busses be V.


Thus,


Relative velocity of bus moving in the direction cyclist = (V-5.55) m/s


Relative velocity of bus moving in opposite direction to the cyclist,


= (V+5.55) m/s


Distance covered by same direction bus = (V-5.55)×1080 m…….(1)


Distance covered by opposite direction bus = (V+5.55)×360 m…..(2)


Since both buses cover same distance (VT), equations (1) and (2) are equal.


⇒ (V-5.55)×1080 m = (V+5.55)×360 m


∴ V = 11.11 m/s


Thus,


Equating, equation (1) = VT


(11.11-5.55)×1080 = 11.11×T


We get, T = 540 s


More from this chapter

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7

Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km/h in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 ms-2. If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them?

 8

On a two-lane road, car A is travelling with a speed of 36 km/h. Two cars B and C approach car A in opposite directions with a speed of 54 km/h each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident?

 10

A player throws a ball upwards with an initial speed of 29.4 m/s.

(a) What is the direction of acceleration during the upward motion of the ball?


(b) What are the velocity and acceleration of the ball at the highest point of its motion?


(c) Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of x-axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion.


(d) To what height does the ball rise and after how long does the ball return to the player’s hands? (Take g = 9.8 ms-2 and neglect air resistance).

 11

Read each statement below carefully and state with reasons and examples, if it is true or false ;

A particle in one-dimensional motion


(a) with zero speed at an instant may have non-zero acceleration at that instant


(b) with zero speed may have non-zero velocity,


(c) with constant speed must have zero acceleration,


(d) with positive value of acceleration must be speeding up.