Question

A boy of mass 60 kg and a girl of mass 40 kg are together and at rest on a frozen pond and push each other apart. The girl moves in a negative direction with a speed of 3 m/s. What must be the final momentum of the boy?

A. 100 kgm/s
B. 120 kgm/s
C. -120 kgm/s
D. 40 kgm/s

Answer 1

Ans

According to the law of conservation of momentum, the total momentum of the system before and after the interaction must be equal. Initially, the momentum of the system is zero since the boy and the girl are at rest. When they push each other, the girl moves in the negative direction with a speed of 3 m/s. Let's assume that the boy moves in the positive direction with a speed of v m/s.

The total initial momentum of the system is:

P_initial = m_boy * 0 + m_girl * 0 = 0

The total final momentum of the system must also be zero since there are no external forces acting on the system. Therefore:

P_final = m_boy * v + m_girl * (-3) = 0

where m_boy = 60 kg, m_girl = 40 kg, and v is the final speed of the boy in m/s.

Solving for v, we get:

60v - 120 = 0

v = 2 m/s

Therefore, the total final momentum of the boy must be:

P_final = m_boy * v = 60 kg * 2 m/s = 120 kg m/s.

So, the total final momentum of the boy must be 120 kg m/s.

Answer 2

B. 120 kgm/s

Step-by-step explanation:

The initial momentum of the system is zero since the boy and the girl are at rest. When they push each other apart, the total momentum of the system remains conserved. Since the girl moves in a negative direction, the boy must move in the positive direction with the same momentum to keep the total momentum of the system zero.

Let's assume the final momentum of the boy is p. According to the law of conservation of momentum,

(initial momentum) = (final momentum)

0 = p + (-40 kg)(-3 m/s)

0 = p + 120 kg m/s

p = -120 kg m/s

Therefore, the final momentum of the boy must be 120 kg m/s in the positive direction, which is answer choice B.