A toy rocket is launched from the top of a building 380 feet tall at an initial velocity of 64 feet per second.

Question

The height of the rocket t seconds after launch is given by the equation S(t)=-16t²+64t+380

when does the rocket reach its maximum height? What is the maximum height?

Answer 1

Hi Tracy.

 

For quadratic functions, the t_max occurs when t = -b/2a

 

For your particular function:

 

S(t) = -16t² + 64t + 380

 

t_max = -b/2a

 

= -64/(2*-16)

 

= -64/-32

 

= 2 sec

 

The max height will be the height that occurs at t_max

 

S(t_max) = -16(2)² + 64(2) + 380

 

= -16(4) + 64(2) + 380

 

= -64 + 128 + 380

 

= 444 ft

 

Hope this helps.

Answer 2

The equation S(t)=-16t²+64t+380 is a parabola that is open downwards. The axis of symmetry is x = -b/2a = -64/2(-16) = 2.

Therefore at t = 2 seconds, the rocket reaches its maximum height.

The maximum height = S(2) = -16(2)² +64(2) +380 = 444 ft