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?

Answer 1

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.