Find the magnitude of the linear momentum of (i) a 7.1 kg bowling ball traveling at 12 m/s and (ii) a 200 kg automobile traveling at 90 km/h. (b) A pool player imparts an impulse of 3.2 N-s to a stationary 0.25 kg cue ball with a cue stick. What is the speed of the ball just after impact?

To find the magnitude of the linear momentum, we use the formula:

Linear momentum = mass × velocity

(i) For the bowling ball:

Mass = 7.1 kg
Velocity = 12 m/s

Linear momentum = 7.1 kg × 12 m/s = 85.2 kg·m/s

(ii) For the automobile:

Mass = 200 kg
Velocity = 90 km/h

To convert the velocity from km/h to m/s, we divide by 3.6:
90 km/h ÷ 3.6 = 25 m/s

Linear momentum = 200 kg × 25 m/s = 5000 kg·m/s

(b) To find the speed of the ball just after impact, we use the equation:

Impulse = change in momentum

Impulse = 3.2 N-s
Mass = 0.25 kg

Change in momentum = impulse = 3.2 N-s

We know that momentum = mass × velocity

So, 3.2 N-s = 0.25 kg × velocity

Solving for velocity:

velocity = 3.2 N-s ÷ 0.25 kg = 12.8 m/s

Therefore, the speed of the ball just after impact is 12.8 m/s.

To find the magnitude of the linear momentum, we can use the formula:

Linear Momentum = mass x velocity

(i) For a 7.1 kg bowling ball traveling at 12 m/s:
Linear Momentum = 7.1 kg x 12 m/s = 85.2 kg·m/s

(ii) For a 200 kg automobile traveling at 90 km/h, the velocity needs to be converted to m/s:
90 km/h = 90,000 m/3600 s = 25 m/s
Linear Momentum = 200 kg x 25 m/s = 5000 kg·m/s

(b) To find the speed of the ball just after impact, we can use the principle of conservation of linear momentum. The impulse exerted on the ball is equal to the change in momentum, and can be calculated using the formula:

Impulse = mass x change in velocity

Given that the impulse is 3.2 N-s and the mass of the cue ball is 0.25 kg:
3.2 N-s = 0.25 kg x change in velocity

Rearranging the equation, we can solve for the change in velocity (final velocity - initial velocity):
change in velocity = Impulse / mass = 3.2 N-s / 0.25 kg = 12.8 m/s

Since the cue ball is initially stationary (initial velocity is 0 m/s), the final velocity is equal to the change in velocity:
Final velocity = change in velocity = 12.8 m/s

Therefore, the speed of the ball just after impact is 12.8 m/s.