Question

A trolley is moving horizontally with a velocity of v m/s w.r.t. earth. A man starts running in the direction of motion of trolley from one end of the trolley with a velocity $1.5$v m/s w.r.t. the trolley. after reaching the opposite end, the man turns back and continues running with a velocity of $1.5$v m/s w.r.t. trolley in the backward direction. If the length of the trolley is L, then find the maximum displacement of the man with respect to earth, measured as a function of time.

Answer 1

The displacement covered by man w.r.t. trolly is zero

Time taken to travel $2L$ distance is $t=\frac{2L}{1.5v}$

Now maximum displacement w.r.t. earth is displacement by trolly w.r.t. ground in time $t$

displacement $d=v.t$

$=v\frac{2L}{1.5v}=\frac{2}{1.5}=\frac{4}{3}m$