If a ball is thrown vertically upward with a velocity of 80 fts, then its height after t seconds is s 80t 16t2.
(a) What is the maximum height reached by the ball?
To find the maximum height, or the maximum point on the graph of s(t)=80t-16t^2, you want to find when the derivative is zero.
- Find the derivative of s(t).
- Set that equal to 0 and solve.
Now you know that the ball reaches its maximum height at t=2.5 seconds.
- Put that value of t into the original equation.
The maximum height of the ball is 100 feet, and it reaches that height 2.5 seconds after it’s thrown.