Word problem

Question

The equation h(t)=40t-16t² describes the height h, in feet, of a ball that is thrown straight up as a function of the time t, in seconds, that the ball has been in the air. At what time does the ball reach it's maximum height? What is the maximum height?

Answer 1

Hello Nina -

 

Perhaps the simplest way to do this is with a graphing calculator. I assume you have one and can use it on such problems. If so, putting the h(t) in as y1 and looking at the graph, you can see that the answer is that at about 1.25 seconds the ball will be 25 ft high. 

 

If you need to do this analytically, you would find the vertex of the quadratic curve at -b/2a and then substitute back into the equation to get the values. The vertex will give you the time value (a function of t) and h(t) is the height. 

 

Here a = -16 and b = 40, the vertex is 1.25 and h(1.25) = 25

 

Hope this helps,

 

Ken