The best batter

Classical Mechanics Level 3

You are in the batter's box in an intermural baseball game. Suppose that the pitcher throws a fast ball at you parallel to the ground, and you hit the ball when its velocity is 35 m/s 35 \text{ m/s} . Then the ball flies to a height of 62.5 m 62.5 \text{ m} above the ground. Find the approximate average force acting on the ball when the contact duration is 1 50 s \frac{1}{50} \text{ s} and the mass of the ball is 0.12 kg. 0.12 \text{ kg.}

Gravitational acceleration is g = 10 m/s 2 . g = 10 \text{ m/s}^2 .

212 N 148 N 297 N 594 N

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Srinivasa Satti by Srinivasa Satti

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1 solution

Dhruv Bhanushali
Apr 11, 2015

Since height reached is 62.5m velocity must have been 35 metres upward.

u = 35i m/s

v = 35j m/s

Magnitude of change in velocity = 35 x sqrt(2) m/s

Magnitude of change in momentum = 0.12 x 35 x sqrt(2) kg m/s

Average force = Change in momentum / Time ~ 297 N

1 Helpful 0 Interesting 0 Brilliant 0 Confused

But how do you know that the ball was travelling directly upwards? You are correct that the vertical component of the velocity must be 35m/s , but you forget that there could be a lateral component to the velocity as well, which would make the total momentum change larger, and therefore the force larger than 297N

Robbie King - 5 years, 12 months ago

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