Applications of Quadratic Equations and Functions

Question

Jo Jo the monkey jumps off a 200-foot cliff into the ocean, so that his height, h, in feet, after t

seconds is given by the function:

h(t) = −16t²! + 160t + 200

What is the maximum height the Jo Jo reaches?

How long is Jo Jo in the air before he hits the water?

Answer 1

h(t) =-16t^2 + 160t +200

h'(t)= -32t +160=0

t =160/32 = 5 seconds reaching maximum height

max h =-16(5)^2+160(5) +200

= -400+800+200= 600 feet maximum height

h(t) =0 =-16^2+160t+200

2t^2 -20t -25 = 0

t = 20/4 + (1/4)sqr(400+200)

= 5+ (5/2)sqr6 = about 5+2.5(2.45)

= 16.125 = 16 1/8 seconds until hitting the ocean