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How do you answer- Determine whether a baseball hit 136ft per sec at an angle of 30 degrees relative to the ground will clear a 10 foot wall 400 feet away?
14lax13
What's missing in all of these numbers is the height of the ball as it leaves the bat.
Let's see what we can determine without it:
-- The ball's vertical speed as it leaves the bat is 136 x [ sin(30) ] = 68 ft/sec.
-- The acceleration of gravity is 32.2 ft/sec2 .
-- At 68 ft/sec, the ball will rise for 68/32.2 seconds, turn around, and drop back to
the height of the bat in the same amount of time. So it's above the height of the
bat for 68/16.1 = 4.224 seconds after the hit.
-- The ball's horizontal speed is 136 x [ cos(30) ] = 117.779 ft/sec.
-- In the 4.224 seconds the ball spends above the height of the bat, it travels
4.224 x 117.779 = 497.5 feet from home plate.
-- The ball most likely does clear the 10-ft wall 400-ft from the plate, since it travels
97.5 ft farther than that before it has dropped back to the height of the bat.
-- I could put a finer point on it by calculating how far the ball drops during the
last 97.5-ft of its horizontal flight. But I don't feel like it right now, and I leave
that refinement to the purists.
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∙ 11y ago
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