Question

A man weighing 80kg is standing on a trolley weighing 320kg. The trolley is resting on a frictionless surface. If the man starts walking on the trolley along its length at speed 1 m/s,

Answer 1

Displacement of man with respect to ground is  3.2 m

Explanation:

Correct statement:

A man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1m/s, then after 4 second his displacement relative to the ground will be?

Solution:

Trolley will move in opposite direction  to man's movement to conserve the momentum.

Let's say the velocity of trolley is v and it's mass is m. Let man's velocity is V and his mass is M, then we have

 m×v = -(M+m)×V..........(1)

We are given

m = 320 kg

M = 80 kg

V= 1 m/s

By substituting these values in (1), we get

m×v = -(M+m)×V

320 x v = - ( 80 + 320) x 1

320 x v = -80 - 320 = -400

v = -400 / 320

v = -0.2 m/s.

Since man has moved for 4 seconds.

Distance moved by trolley  = -0.2×4 = -0.8 m  

man has moved 4 m but trolley has moved 1 m in opposite direction.  

Hence displacement of man with respect to ground is 4  -0.8 = 3.2 m

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