at what time will the toy rocket reach its maximum height?

Question

a toy rocket is fired straight into the air. the rocket has an initial velocity of 48 feet per second and its height is modeled by the equation h(t)=480t-16t^2, where h is the height (in feet) and t is the time (in seconds). at what time will the toy rocket reach its maximum height/

Answer 1

So, if we imagine the equation for the height of the rocket we see that we have the equation for a parabola. Knowing this, we recall that parabola's have the standard form ax²+bx+c. 

 

So, 

a=(-16)

b=480

c=0

 

We may also recall that the x-coordinate (t in our case) for the vertex of a parabola occurs at (-b)/(2a) ==> (-480)/(-32)=15. So our vertex occurs at t=15s.

 

The height at this time is h(15)=480(15)-16(15)² ==> h(15)=7200-3600

 

So h(15)=3600ft which is the highest point of the rocket's travel.