(i) a 0.145-kg baseball pitched at 31.0 m/s is hit on a horizontal line drive straight back at the pitcher at 46.0 m/s. if the contact time between bat and ball is 5.00 × 10^–3 s, calculate the force (assumed to be constant) between the ball and bat.

The force between the ball and the bat = 2233 N

Explanation:

Force: This can be defined as the product of force and its acceleration.

The S.I unit of Force is Newton (N)

F = ma Equation 1

Where F = Force , m = mass of the ball, a = acceleration of the ball.

where

a = (v-u)/t Equation 2

Where v = final velocity of the ball, u = initial velocity of the ball, t = time of contact between the ball an the bat.

Given: v = 46 m/s u = - 31 m/s (it hit an horizontal line drive back at the pitcher), t = 5×10⁻³ s

Substituting these values into equation 2,

a = [46-(31)]/(5×10⁻³ )

a = 77×10³/5

a = 15.4×10³ m/s².

Also given m = 0.145 kg

Substituting into equation 1,

F = 0.145(15.4×10³ )

F = 2233 N

Thus the force between the ball and the bat = 2233 N