Question

A 70kg girl jumps out of a moving boat of mass 30 kg onto the bank with a velocity of 5 m/s. At which velocity does the body begin to move backward?

a) 5 m/s
b) 2 m/s
c) 3 m/s
d) 1 m/s

Answer 1

The body begins to move backward at a velocity of -11.67 m/s.

Step-by-step explanation:

To determine the velocity at which the body begins to move backward, we need to apply the law of conservation of momentum.

The momentum of the girl before jumping off the boat is equal to the momentum of the boat and girl system after she jumps.

Given:

Mass of the girl (mg) = 70 kg

Mass of the boat (mb) = 30 kg

Initial velocity of the boat and girl (vi) = 0 m/s

Final velocity of the girl (vf) = 5 m/s

Final velocity of the boat (Vf) = ?

Using the conservation of momentum equation:

mg * vi + mb * vi = mg * vf + mb * Vf

Substituting the given values:

(70 kg * 0 m/s) + (30 kg * 0 m/s) = (70 kg * 5 m/s) + (30 kg * Vf)

Simplifying the equation:

0 = 350 kg*m/s + 30 kg * Vf

30 kg * Vf = -350 kg*m/s

Vf = -350 kg*m/s / 30 kg

Vf = -11.67 m/s

Since velocity refers to speed and direction, the body begins to move backward at a velocity of -11.67 m/s.