1. A baseball with a mass of 140 g is pitched so that it crosses home plate with
ID: 1781825 • Letter: 1
Question
1. A baseball with a mass of 140 g is pitched so that it crosses home plate with a speed of 92.0 mph at an angle of 18.4O below the horizontal. It is hit directly back up the middle of the field with a speed of 81.0 mph at an angle of 41.3O above the horizontal. Find: (a) the impulse (magnitude and direction) delivered to the ball by the bat, and (b) the magnitude of the average force on the ball, if the bat was in contact with the ball for 6.40 ms.
Answer: (a) 10.6 N-s, 29.1 degrees above horiz (b) 1660 N
Please show work with pictures!
Explanation / Answer
a)
m = mass of the ball = 0.14 kg
vi = initial velocity = 92 Cos18.4 i - 92 Sin18.4 j = 87.3 i - 29.03 j
vf = final velocity = 81 Cos41.3 i + 81 Sin41.3 j = 60.85 i + 53.5 j
impulse is given as
I = m (vf - vi) = (0.14) ((60.85 i + 53.5 j) - (87.3 i - 29.03 j)) (0.45) = (0.14) (0.45) (- 26.45 i + 82.53 j) = - 3.7 i + 11.6 j
magnitude of impulse : (0.45) sqrt((- 3.7)2 + (11.6)2) = 12.2 x 0.45 =
direction : 180 - tan-1(11.6 /3.7) = 107.7 deg
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