Baseball Pitch, continued

Question: How long was the ball in the air?

Answer:

Notice that cosine of a small angle is close to unity, so the time is about R/v.

Question: What was highest point?

Answer:

• Easy, it is y when t = 0.723/2, y = 26.5 sinq t - 4.9t² = 26.5 sin7.69° (0.362) - 4.9 (0.362)²= 0.642 m
• Actually you have to aim 2.57 m (about 8.4 feet) above the direct horizontal line because 4.9t² = 2.57 m for t = 0.723 s.
• In general an object in flight drops gt² from where it would have been in a straight line trajectory.
• Since all objects drop with the same acceleration, independent of their velocity, this leads to an interesting demonstration: