2-14. A girl throws a ball into a bucket with a horizontal velocity at point A, whose height is . The width of the bucket is , and the distance between the front edge of the bucket and the girl is . If the coefficient of restitution follows a normal distribution , determine the likelihood that the ball reaches the target. Neglect the height of the bucket.

Solution:

From A to B

At B:

From B to C

and

Thus,

Finding the distance the ball travels

Finding mean

Solving the probability

Therefore, the probability that the ball gets into the bucket is 0.73. Ans.