A basketball is shot with an initial vertical velocity of 24 ft/s from 6 ft. above the ground. At what time will the basketball reach its maximum height?

Question

Need the steps on how to do this equation

Answer 1

The general projectile quadratic model is: h(t) = -16t² + v₀t+h₀.  The -16 is just a constant based on gravitational force, the middle term is the velocity, and the constant is the initial height.

 

If we plug in the numbers, we get h(t) = -16t² + 24t + 6

 

There are a couple of ways to solve this problem.  If you have a graphing calculator, you plug in the function and find the vertex.  The x coordinate of the vertex will tell you what time at the maximum height.  

 

If you want to calculate the time manually, just find the axis of symmetry:

 

x = -b/2a = -24/-32 = 0.75.

 

So it takes 0.75 seconds for the basketball to reach maximum height.