A trolley is moving horizontally with a constant velocity of v( m / s ) w.r.t. the earth. A man starts running from one end of the trolley with a velocity 1.5 v( m / s ) w.r.t. to trolley. After reaching the opposite end, the man returns 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 the earth during the process is (p L/q). Find (p+q)

Question

A trolley is moving horizontally with a constant velocity of v( m / s ) w.r.t. the earth. A man starts running from one end of the trolley with a velocity 1.5 v( m / s ) w.r.t. to trolley. After reaching the opposite end, the man returns 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 the earth during the process is (p L/q). Find (p+q) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Time taken by the man to return to its starting point on trolley is t=(2 L/1.5 v) Displacement of the man w.r.t. the earth during this process is S=v × t=v × (2 L/1.5 v)=(4 L/3) m

Time taken by the man to return to its starting point on trolley is t=1.5v2L​ Displacement of the man w.r.t. the earth during this process is S=v×t=v×1.5v2L​=34L​m

Time taken by the man to return to its starting point on trolley is
$t = \frac{2 L}{1.5 v}$
Displacement of the man w.r.t. the earth during this process is
$S = v \times t = v \times \frac{2 L}{1.5 v} = \frac{4 L}{3} m$