Question

A trolley is moving horizontally with a constant velocity of v m/s w.r.t. earth. A man starts running from one end of the trolley with a velocity 1.5v m/s w.r.t. to trolley. After reaching the opposite end, the man return back to starting end and continues running with a velocity of 1.5 v m/s w.r.t. the trolley in the backward direction. If the length of the trolley is L then the displacement of the man with respect to earth during the process will be:

(A) 2.5L
(B) 1.5 L
(C) 5L/3
(D) 4L/3

Answer 1

The total displacement of the man with respect to Earth after running to the end of a moving trolley and returning is 3L/5, where L is the length of the trolley.

Step-by-step explanation:

The displacement of the man with respect to Earth during the process in which he runs across a trolley moving with a constant velocity v m/s and returns with a velocity of 1.5v m/s with respect to the trolley must be calculated taking into account relative motion. Since the trolley is moving with a velocity v m/s with respect to Earth and the man is moving with a velocity of 1.5v m/s with respect to the trolley when he runs across it, his velocity with respect to the Earth is the sum of these two velocities, or 2.5v m/s. As he returns, his velocity with respect to the Earth becomes v - 1.5v which is -0.5v m/s, indicating he is moving in the opposite direction to the trolley's motion.

The total displacement is the sum of the displacements during both the forward and return trips. On the first trip, he covers a distance L with a velocity of 2.5v m/s, and on the return trip, he covers the same distance L with a velocity of -0.5v m/s. Thus, the displacement during the forward trip is L and during the return trip is -L/5 (L times -0.5v/v), which sum to 4L/5 + (-L/5) = 4L/5 - L/5 = (4L - L) / 5 = 3L/5. Hence, his total displacement with respect to Earth after completing both trips is 3L/5.