Q. 93.7( 113 Votes )
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?
Speed of the cyclist, v = 20 km/h = 5.55 m/s
Time period for bus moving in the same direction= 18 min = 1080 s
Time period for bus moving in opposite direction=6 min = 360 s
Let, The velocity if the buses be V.
Relative velocity of bus moving in the direction of 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
Equating, equation (1) = VT
(11.11-5.55)×1080 = 11.11×T
We get, T = 540 sThe buses move with a speed of 11.11 m/s or 40kmph and the ply after every 540 s or 9 mins
Rate this question :
A ball falls on the ground from a height of 2.0 m and rebounds up to a height of 1.5 m. Find the coefficient of restitution.HC Verma - Concepts of Physics Part 1
Two stones are thrown up simultaneously from the edge of a cliff 200 m high with initial speeds of 15 m/s and 30 m/s. Verify that the graph shown in Fig. 3.27 correctly represents the time variation of the relative position of the second stone with respect to the first. Neglect air resistance and assume that the stones do not rebound after hitting the ground. Take g = 10 m/s2. Give the equations for the linear and curved parts of the plot.
NCERT - Physics Part-I
At a metro station, a girl walks up a stationary escalator in time t1 . If she remains stationary on the escalator, then the escalator take her up in time t2. The time taken by her to walk up on the moving escalator will bePhysics - Exemplar
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).NCERT - Physics Part-I
A uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval. Show the variation of its acceleration with time. (Take acceleration in the backward direction as positive).Physics - Exemplar
The velocity-displacement graph of a particle is shown in Fig. 3.5.
(a) Write the relation between v and x.
(b) Obtain the relation between acceleration and displacement and plot it.
Physics - Exemplar