Final answer:
In this case, the rocket reaches a maximum height of 320 meters.
None of the given options is correct
Step-by-step explanation:
To find the rocket's maximum height, we need to determine the vertex of the quadratic function S(t) = -5t² + 80t, where S represents the height of the rocket and t represents time in seconds.
The vertex of a quadratic function is given by the formula t = -b / (2a), where a and b are the coefficients of the quadratic equation. In this case, a = -5 and b = 80.
t = -80 / (2 * -5)
t = -80 / -10
t = 8
Substituting this value of t back into the equation, we can find the maximum height:
S(8) = -5(8)² + 80(8)
S(8) = -5(64) + 640
S(8) = -320 + 640
S(8) = 320
Therefore, the rocket reaches a maximum height of 320 meters.
None of the given options is correct
Your question is incomplete, but most probably the full question was:
A rocket is fired upward with an initial velocity v of 56.8 m/s.The quadratic function S(t)=−5t²+80t can be used to find the height s of the rocket, in meters, at any time t in seconds.
Find the rocket's maximum height.
a. The rocket reaches a maximum height of 57 meters.
b. The rocket reaches a maximum height of 576 meters.
c. The rocket reaches a maximum height of 5,760 meters.
d. The rocket reaches a maximum height of 57,600 meters.