Question

with what speed must a ball be thrown vertically upward in order to rise to a height of 50 ft ? how long will it be in the air

Answer 1

Let's find the time needed to reach the height of 50 ft (= 15.24m) with the minimum required speed (so that the velocity of a ball be equal to zero at the top point).

H = gt²/2 ==> t = √(2H/g) = √(2*15.24[m]/9.8[m/s²]) ≈ 3.11[s].

So, initial velocity of a ball must be

V = gt = 9.8[m/s²]*3.11[s] = 30.48[m/s].