Question

A boy of mass $60kg$ running at $3m/s$ jumps on a trolley of mass $140kg$ moving with a velocity of $1.5m/s$ in the same direction. What is their common velocity?

Answer 1

Step 1: Given data

Given the mass of the boy (m)$=60kg$
The initial velocity of the boy (u)$=3m/s$
The mass of the trolley (M)$=140kg$
The initial velocity of the trolley (U)$=1.5m/s$
Let the common velocity of the boy and trolley$=vm/s$

Step 2: Formula used and calculation for velocity

According to the law of conservation of momentum the momentum must be conserved before and after the collision.
Therefore initial momentum must be equal to final momentum.
$$\begin{gathered} p_B+p_T=p_{B+T}-----equation\left(I\right) \\ {p}_B=initialmomentumoftheboy \\ {p}_T=initialmomentumofthetrolley \\ {p}_{B+T}=finalmomentumofthebodyandtrolley \\ Substitutingthevalueofm,u,M,andUinequation\left(I\right)weget- \\ \left(60\right)\times \left(3\right)+\left(140\right)\times (1.5)=\left(200\right)\times \left(v\right)\{p=mv\} \\ 180+210=200v \\ or200v=390 \\ v=\frac{390}{200} \\ v=1.95m/s \end{gathered}$$

Hence the combined velocity of the body and trolley is $1.95m/s.$