With what speed must a ball be thrown vertically up in order to rise to a height of 50 ft?

Question

How long will it be in the air?

Answer 1

a) v = √(2gy)

b) t = 2*√(2y/g)

Answer 2

For the initial calculation, assume no friction from the air. In that environment, the speed of the ball going up matches the speed on it's way down, so we can simply do the calculation for a drop of the ball for the speed and then double the time in of the drop for the total time in the air. The formula is

distance = initialSpeed x time + (1/2) acceleration x time^2

50 = 0 + 1/2 (32) x time^2
time^2 = 50 /16
time = SQRT(50/16) ~= 7/4 = 1.75 seconds

To get speed:

Speed = acceleration x time
Speed = 32 x (7/4) = 8 x 7 = 56 ft per second

For time, double the time to drop: ~ 2.5 seconds.

speed =