Answer:
The velocity of the ball after the collision is 5.39 m/s
Explanation:
Hi there!
To solve this problem, we will use the conservation of momentum: the momentum of the system ball-pin remains the same before and after the collision. The momentum of the system is calculated as follows:
momentum before the collision (initial momentum) = mb · vb1 + mp · vp1
momentum after the collision (final momentum) = mb · vb2 + mp · vp2
Where:
mb = mass of the ball = 7.05 kg
vb1 = velocity of the ball before the collision = 8.24 m/s
mp = mass of the pin = 1.52 kg
vp1 = velocity of the pin before the collision = 0 m/s.
vb2 = velocity of the ball after the collsion = unknown.
vp2 = velocity of the pin after the collision = 13.2 m/s
Since momentum is conserved, then:
initial momentum = final momentum
mb · vb1 + mp · vp1 = mb · vb2 + mp · vp2
Solving for vb2:
mb · vb1 + mp · vp1 - mp · vp2 = mb · vb2
(mb · vb1 + mp · vp1 - mp · vp2) / mb = vb2
Since the pin is initially at rest, vp1 = 0:
(mb · vb1 - mp · vp2) / mb = vb2
(7.05 kg · 8.24 m/s - 1.52 kg · 13.2 m/s) / 7.05 kg = vb2
vb2 = 5.39 m/s
The velocity of the ball after the collision is 5.39 m/s
