change in momentum?

Question

a 60 kg student on in-line skates is playing with a 25 kg ball. If the student is initially at rest then catches the ball thrown to the right at 4.5 m/s. Explain the change in the student's momentum?

a. no change
b. the student's momentum will be to the right
c. the momentum will be zero
d. the student's momentum will increase while the ball's momentum will decrease

Answer 1

Momentum is always conserved in collisions.

Initial momentum: ( 60 kg ) ( 0 ) + ( 25 kg ) ( 4.5 m/s )
Final momentum: ( 60 + 25 kg ) ( v )

Set these expressions equal and solve for v. You will find that both (b) and (d) are true. Ignore the fact that anyone trying to catch a 25-kg ball moving at 4.5 m/s deserves what they get.

Answer 2

In this problem our system consists of the ball and the student.
According to the law of conservation of momentum, the total momentum of the system before = total momentum of the system after.
Hence,
60kg(0) + 25kg(4.5m/s) = (60kg + 25kg)Vbs
where, Vbs is the velocity of the ball and student combined.
Solving,
Vbs = (112.5 kgm/s)/(85kg)Vbs
Vbs = 1.32 m/s

Δp student = m(Vbs - Vis), where Vbs = combined velocity of the ball and student; m = mass of student
Vis = initial velocity of the student = 0
Δp = 60kg(1.32 m/s - 0)
Δp = 79.2 kgm/s

Δp ball = m(Vbs - Vib), where Vib = initial velocity of the ball, and m = mass of ball.
Δp = 25 kg(1.32 m/s - 4.5 m/s)
Δp = -79.2kgm/s

So, answer is d.

teddy boy