Patricia's height in meters above the water t seconds after diving from a diving board into a pool can be modeled by f(t)-5t^2+20t+5. What's Patricia's maximum height above the water?

Question

the height h(t) in feet of an object thrown into the air with an initial upward velocity of 63 feet per second is given by the formula h(t)=-16t^2+63t+20 where t is the time in seconds. What's the height of the object after 2 seconds?

Answer 1

Question 1.

f(t)=-5t²+20t+5=5(-t²+4t+1)=

5(-t²+4t-4+4+1)=

5(5-(t-2)²). This is maximum when t=2, and the maximum height is therefore 5×5=25m.

Question 2.

h(2)=-64+126+20=82ft.