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## Homework Statement

During the first 50 s of a rocket's flight, the rocket is propelled straight up, so that in t seconds its height s is s(t) = t^3/sqrt 10 ft.

a) How high does the rocket travel in 50 s?

b) What is the average velocity of the rocket during the first 50 s?

c)What is the average velocity of the rocket during the first 125 ft?

## Homework Equations

s(t) = t^3/sqrt 10 ft

v(t) = 3t^2/sqrt 10

## The Attempt at a Solution

a) Pretty straightforward: s(50)= 50^3/sqrt 10

= 125000/sqrt10

≈39,528.47 ft

b) average velocity = distance traveled/time elapsed

= 39528.47/50

≈790.57ft/s (I have a feeling this may be wrong)

c) 125ft=t^3/sqrt10

t=cbrt125*sqrt10

= 7.34s

Average = 125ft/7.34s

= 17.03ft/s (I also think this may be wrong)

If I was an error, where would I be? I feel like a rocket traveling at 17ft/s after 7 seconds may be a tad on the low side.