**Sample Problem**

A pitched 140 g baseball, in horizontal flight with a speed Vi of 39.0, is struck by a bat. After leaving the bat, the ball travels in the opposite direction with speed VI’ also 39.0.

(a) What impulse J acts on the ball while it is in contact with the bat during the collision?

SOLUTION: The Key Idea here is that we can calculate the impulse from the change it produces in the ball’s linear momentum, using for one-dimensional motion. Let us choose the direction in which the ball is initially moving to be the negative direction.

(b) The impact time for the baseball-bat collision is 1.20 ms. What average force acts on the baseball?

SOLUTION: The Key Idea here is that the average force of the collision is the ratio of the impulse J to the duration III of the collision.

(c) Now suppose the collision is not head-on, and the ball leaves the bat with a speed VI of 45.0 mls at an upward angle .

SOLUTION: The Key Idea here is that now the collision is two-dimensional because the ball’s outward path is not along the same axis as its incoming path.

Instead, we can evaluate in component form. To do so, we first place an xy coordinate system as shown in . Then along the x axis we have

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