A baseball is tossed at a steep angle into the air and makes a smooth parabolic path. Its time in the air is t and it reaches a maximum height h. Assume that air resistance is negligible.

Question

a.) Show that the height reached by the ball is gt2 (square) /8.
b.) If the ball is in the air for 4 seconds, show that the ball reaches a hieght of 19.6m.
c.) If the ball reaches the same height as when tossed at some other angle, would the time of flight be the same?

Answer 1

a) If the time in the air is t, it spends t/2 going up and t/2 coming back down. The distance it falls in time t/2 is
(1/2)*g*(t/2)^2 = gt^2/8
b) gt^2/8 = 9.8* 16/8 = 19.6 m
c) The formula linking max height to time in the air is independent of the angle thrown. So the answer is "yes".