Question
A toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function f(t)=-16t^2+48t , where t is the time in seconds since the rocket was shot and f(t) is the rocket’s height. What is the maximum height the rocket reaches?
16ft
36ft
48ft
or 144 ft
16ft
36ft
48ft
or 144 ft
Answers
Damon
Well, that is a parabola. Where is the vertex?
-16 t^2 + 48 t = h
16 t^2 - 48 t = -h
t^2 - 3 t = -(1/16)h
t^2 - 3 t + 9/4 = -(1/16)h + 9/4
(t - 3/2)^2 = -(1/16)(h - 36)
ah ha, hits the vertex at the top when t = 1.5 seconds and h = 36 feet
-16 t^2 + 48 t = h
16 t^2 - 48 t = -h
t^2 - 3 t = -(1/16)h
t^2 - 3 t + 9/4 = -(1/16)h + 9/4
(t - 3/2)^2 = -(1/16)(h - 36)
ah ha, hits the vertex at the top when t = 1.5 seconds and h = 36 feet
alex
thanks!!
Damon
You are welcome.