Question

Two boats both having a mass of 150 $kg$ including passengers in it are rest. A sack of mass $50kg$ makes 1st boat having total mass of $200kg$. It is thrown to the second boat with a velocity whose horizontal component is $2{ms}^{-1}$, relative to water. Calculate the distance (in $m$) between the boat $8.5s$ after the throw if the sack spent $0.5s$ in the air. Neglect the resistance of air and water.

Answer 1

Mass of boat 1 = 150kg and mass of boat 2 = 200kg.

Initially, boat 1 had 200kg at rest. Let the velocity of boats be v1, v2.

Conservation of linear momentum for boat1:

$200kg\times 0m/s=150kg\times v1+50kg\times 2m/s$

$v1=-2/3m/s$

Distance travelled by boat in $8.5s=8.5v1=17/3m$

Conservation of linear momentum for boat2:

$150kg\ast 0m/s+50kg\ast 2m/s=200kg\ast v2$

$v2=1/2m/s$

It takes $0.5s$ for sack to reach boat 2.

Distance travelled by boat in $8s=8v1=4m$

Distance between boats = $4m+17/3m=29/3m$