Quadratic equation graphing

Question

The function h(t) gives the height and feet of a ball t seconds after is thrown upward from the roof of a 64 foot tall building. How many seconds after the ball is thrown does it reached it’s maximum height? What is the balls maximum height?

Answer 1

This problem is missing some details, but we'll insert them as variables.

The ball is thrown upward from a 64 foot tall building, with initial velocity v₀. How many seconds after the ball is thrown does it reach its maximum height?

While this is labeled as an algebra 2 problem, this is a classical physics problem: 1D free-fall. In free fall, the velocity of an object is given by v(t) = v₀ - gt, where g is the acceleration due to gravity.

Thinking about the motion of the ball physically, you will note that it slows down until it reaches its highest point, then changes direction, and builds up its velocity downward. At the highest point, then, the velocity of the ball is 0.

Plugging this into our equation, we get 0 = v₀ - gt -> t = v₀/g.

The ball's height is given by h(t) = 64 + v₀t - .5gt² , using the constant-acceleration equation for position. Plug in the time t =v₀/g to obtain the maximum height.