Question

A 140 g baseball is moving horizontally to the right at 40 m/s when it is hit by the bat. The ball flies off to the left at 45 m/s , at an angle of 25∘ above the horizontal.

a)What is the magnitude of the impulse that the bat delivers to the ball? Express your answer to two significant figures and include the appropriate units.

b)What is the direction of the impulse that the bat delivers to the ball? Express your answer to two significant figures and include the appropriate units.

Answer 1

Impulse = change in momentum

Here, we assume that original direction of ball is positive.

The final direction will have two components

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In x - direction

Impulse , J_x = 0.140 ( -45 * cos 25 - 40)

J_x = - 11.31 kg.m/s

In y - direction ( note there was no initial velocity in y direction)

J_y = 0.140 ( 45 * sin 25 - 0)

J_y = 2.662 m/s

so,

J = sqrt ( Jx² + Jy²)

J = 12 Kg.m/s

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Part b

direction angle is found as

angle = arctan ( 2.662 / - 11.31)

angle = 13.244 degree ( above negative x - axis)