Question

A toy rocket is launched straight up from the top of a building. The function that models the height as a function of time is h(t)=-16t^2+200t+50
At what time will the rocket reach the maximum height?

A toy rocket is launched straight up from the top of a building. The function that models the height as a function of time is
. At what time will the rocket reach the maximum height?

Answer 1

To find the time at which the rocket reaches the maximum height, we need to find the vertex of the parabolic function h(t)=-16t^2+200t+50.

The vertex of a parabola in the form y=ax^2+bx+c is given by the equation x=-b/(2a).

In this case, a=-16 and b=200. Plugging these values into the equation, we get:

t = -200 / (2 * -16)
t = -200 / -32
t = 6.25

Therefore, the rocket will reach the maximum height at t=6.25 seconds.