Question

After a 60-kg person steps from a boat onto the shore, the boat moves away with a speed of 0.60 m/s with respect to the shore. If the same person steps from the shore onto the boat, the person and the boat move away from the shore with the speed of 0.40 m/s. Assume that the initial speed of the person with respect to the shore is the same in both cases and that the person is moving in a horizontal direction. Determine the Mass of the boat and the speed of the person.

Answer 1

Answer:m=80 kg

Explanation:

Given

mass of Person $M=60 kg$

When Person Steps From boat onto shore boat moves away to 0.6 m/s away from shore

let v be the velocity of Person and m be the mass of boat

Conserving momentum

$M v-0.7 m=0$

$M v-0.7 m=0$

$60 v=0.7 m$----1

When Person step on to boat, boat moves on to left 0.4 m/s towards left

$Mv=(M+m)\cdot 0.4$

$60 \cdot v=(60+m)\cdot 0.4$---------2

using 1 and 2

$60 v=(60+85.71 v)\cdot 0.4$

$v=0.933 m/s$

therefore $m=79.99\approx 80 kg$