Question

A ball is thrown directly upward from a height of 3 ft with an initial velocity of ​20 ft/sec. The function ​s(t)=-16t^2+20t+3 gives the height of the​ ball, in​ feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.

Answer 1

#1: s'(t)= -32t+20

#2: -32t+20=0

t=2/3

#3: s(2/3)=-16(2/3)^2+20(2/3)+3=83/9

Explanation:

first find the derivative of the original funtion #1

set the equation equal to 0 because when s't=0 is the maximum height

put the t at highest point into the funtion to solve for distance