Let's first understand what information is given to us:

Mass of cricket ball = 0.145kg

Initial speed of the ball = v_i = 38.2 m/s

Final speed of the ball = v_f = 0 m/s

Distance travelled by the ball as it is decelerating = S = 0.135m

We know that F = m a = 0.145 x a N. Therefore, once we determine the acceleration of the ball in m/s^2, we can easily determine the force applied on it.

Let's recall the equations of motion (https://isaacphysics.org/concepts/cp_eq_of_motion).

a = (v_f - v_i)/t

S = v_i t + 1/2 a t^2

v_f^2 = v_i^2 + 2 a S

Of the three equations, only the third allows us to calculate acceleration from the information given.

0 = 38.2^2 + 2 a S => a = -5404.6 m/s^2. We will disregard the sign as the sign indicates that the ball is slowing down.

Therefore, the force applied by Brian Lara on the ball = 0.145 x 5404.6 m/s^2 = 783.7 N.

I found an answer from www.khanacademy.org

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