Question

A 0.5 kg ball is initially at rest on a frictionless surface. It is struck by a bat, and the bat exerts an average force of 50 N on the ball for a duration of 0.1 seconds. What is the impulse experienced by the ball, and what is its resulting velocity?

Answer 1

The ball experiences an impulse of 5 kg·m/s and ends up with a resulting velocity of 10 m/s after being struck by the bat.

Step-by-step explanation:

The impulse experienced by the ball when struck by a bat is the product of the average force applied to the ball and the duration of time that force is applied. The formula for impulse (I) is I = F × t, where F is the force in newtons (N) and t is the time in seconds (s). In this case, the impulse I would be equal to 50 N multiplied by 0.1 s, resulting in an impulse of 5 kg·m/s.

To find the resulting velocity (v) of the ball, we use the change in momentum (∆p) which is equal to the impulse. The initial momentum (pi) is zero because the ball is initially at rest. Hence, the final momentum (pf) equals the impulse. We can use the formula ∆p = m × v to solve for v. Here m is the mass of the ball in kilograms (kg) and v is the velocity in meters per second (m/s). The mass of the ball is 0.5 kg, and the impulse is 5 kg·m/s, so the velocity v = ∆p/m = 5 kg·m/s / 0.5 kg, resulting in a final velocity of 10 m/s.