Question

Check my work

A catapult launches a boulder with an upward velocity of 184 feet per second. The height of the boulder, h, in feet after t seconds is given by the function h(t)=-16t^2+184t+20. What is the boulder's maximum height? How long does it take the boulder to reach its maximum height? Round to the nearest hundredth if necessary.

A. Reaches a maximum height of 11.6 feet after 5.75 seconds.
B. Reaches a maximum height of 549 feet after 11.5 seconds.
C. Reaches a maximum height of 549 feet after 5.75 seconds.
D. Reaches a maximum height of 23.2 feet after 11.6

Answer 1

I got C

Answer 2

@Aveline

Answer 3

i think you are right but im not positive

Answer 4

okay so this is height as a function of time right?

Answer 5

hmm. this is what i'm getting.

We can take the derivative a of this function and set it equal to zero then plug the number back into our original problem.

our original function gives us position with respect to time, but we can easily find the velocity with respect to time which is the derivative.

we know that the object is it's going to slow down until it reaches it's maximum height where the velocity is zero.

\[\frac{ dh }{ dt } -16t^{2}+184t+20 = -32t+184 \]

\[-32t+184 = 0 \]

\[t = \frac{ -184 }{ -32 } = 5.75 s \]


\[f(5.75) = -16(5.75)^{2}+184(5.75)+20 = 549~ft \]

Answer 6

So I got it right?

Answer 7

ya like i said

Answer 8

lol

Answer 9

Thank you