Question

An 80kg person is at rest on a 500Kg boat. He throws a 10Kg package at a speed of 15m/s. What is the magnitude of velocity of the boat

Answer 1

Given:

Mass of the person on the boat = 80 kg.

Mass of the boat = 500 kg

Mass of the package = 10 kg

Speed with which the man throws the packet = 15 m/s

To Find:

Magnitude of the speed of the boat = ?

Solution:

We will use here the momentum of conservation to get the value of speed of the boat.

Since, the 10 kg package is released by the man from the boat. So, after throwing this package there will be 10 kg loss in the mass of the system of man + boat.

Also, the initial speed of the system is zero. So, from momentum conservation we have:

Initial momentum of the system = final momentum of the system

$(80+500)\times 0 = 10\times 15 - (80+500-10) \times v$

Since, the velocity of boat will be opposite to the direction of velocity of the thrown package, so we have taken negative sign.

$0=10\times 15- 570\times v\\570v=150\\v=\frac{150}{570}\\v=0.26$

Hence, the velocity of boat is 0.26 m/s and in opposite direction to the speed of thrown package.