College Algebra Word Problem

Question

If an object is projected upward from ground level with an initial velocity of 160 ft per sec, then its height in feet after t seconds is given by s(t)= −16t squared +160t. Find the number of seconds it will take to reach its maximum height. What is this maximum height?
The object will take
nothing second(s) to reach its maximum height.

Answer 1

s(t) = -16t^2 + 160t take the derivative and set = 0 to find max height time

16t^2 = 160

t^2 = 10

t = sqr10 = 3.16 seconds to reach max height

max height = s(sqr10) = -16(10) + 160(sqr10) = about 506-160 = 346 feet