A tennis player hits a ball 3 feet above the ground with a velocity of 60 ft/sec. What is the maximum height the ball will reach?

Question

If an object has been thrown or launched, the formula to model the height of the object t seconds after it has been launched is: Remember V is velocity and h is the starting point /height.

h(t) = -16t2 + v0t + h0.

Answer 1

h=-16t^2 +60t + 3

h' =-32t +60=0

t= 60/32 = 15/8 = 1 7/8 second to reach maximum height

max h = -16(15/8)^2 +60(15/8) + 3 = 225/4 +3 = 56.25 + 3 = 59.25 feet

that formula assumes the initial velocity, vo, is the upward velocity, as if the tennis player hit the ball vertically upward and it went up nearly 60 feet then came straight down and hit the tennis player on the head.

if the tennis player is aiming at the top of the net, which is more likely about 3 feet, you get a very different answer, closer to max h = 3 ft. That's with vo, initial velocity closer to a horizontal velocity.