Question

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 the air resistance is negligible.

(a) show that the height reached by the ball is gt^2/8.

(b) if the ball is in the air for 4 seconds, show that the ball reaches a height of 19.6m.

(c) If the ball reached the same height as when it is tossed at some other angle, would the time of flight be the same?

Answer 1

Answer:

a)$gt^2/8$

b) 19.6 m

c) Yes.

Explanation:

a) let suppose total time of flight of base ball is t meaning it took t/2 time to reach top and t/2 to come down on the ground.

So, distance it traveled in first t/2 time =  $\frac{1}{2}g (t/2)^2$

= $gt^2/8$

b) for t= 4 sec

height h= $gt^2/8$

h=  $9.8\times4^2/8$

h= 19.6 m

c) The formula connecting maximum height to the time in the air is independent of the angle of throw. So, If the ball reached the same height as when it is tossed at some other angle,  the time of flight would be be the same.