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

Given S(t) = -16 t ² +160 t

 

For S to be maximum its first derivative with respect to time should be zero

 

dS/dt =0

 

-16x2t +160x1 = 0

 

-32t =-160

   t=5 sec  which is time it takes to reach maximum height

To get maximum height 

 

S= -16x5x5 +160x5 = -800 +400 = 400 ft