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A ball was hit and landed 180m away with max height of 21.3m. What is its initial velocity?
Babe Ruth hit a home run that was estimated to have landed 180 meters from home plate with a maximum height of 21.3 meters. What was the initial velocity of the ball? Work and justification please.
1 Answer
- Anonymous1 decade agoFavorite Answer
First we need to find the time the ball was in the air. We can find the time it took to fall 21.3 meters using s=1/2 * a * t^2, and since compensating for air resistance is very complicated, we won't do that, and assume that the ball was in the air for 2 times the time it took to fall.(We are also assuming that the ball was hit from ground level, since you did not give the height of the ball when it was hit).
So, once you find the time the ball was in the air, and you know it travelled horizontally 180 feet in that time, you can find the horizontal speed by dividing 180 by the time.
Next you want to calculate the vertical speed at impact. That will be the same as the speed it reaches when it hits the ground, or 9.8 * t
Lastly, you need to combine the vertical and horizontal speeds using Pythagoras' rule S^2 = Sqrt( Vs^2 + Hs^2)
the speed squared = the sqrt of the sum of the squares of the horizontal and vertical speeds.