During the first 40 seconds of a rocket flight, the rocket is propelled straight

Question

During the first 40 seconds of a rocket flight, the rocket is propelled straight up so that t seconds it reaches a height of s = 0.5t3 ft. a) How high does the rocket travel in 40 seconds? _______ft b) What is the average velocity of the rocket during the first 40 seconds? _________ ft/s c) What is the average velocity of during the first 1000 ft of its flight? ________ft/s (Round the time to three decimal places. Round the velocity to one decimal place. a) What is the instantaneous velocity of the rocket at the end of 40 seconds? __________ f/s

Explanation / Answer

A) s=.5(40)^3=32,000 ft

B) The avg velocity can be found by the equation (Change in distance)/(change in time) so

V average=32,00(m/s)/40s

C)We can find how how long the rocket takes to travel 1000 ft with the equation s=.5t^3.

We get 1,000=.5t^3 which gives t=12.6

The equation for velocity can be found by integrating position (s=.5t^3) which gives V=1.5t^2. We plug in our t value (12.6) to get the velocity.

V=1.5(12.6)^2=238m/s

D) Here we use the same velocity equation we used in part C (V=1.5t^2). Simply plug in the time you want to find the velocity for into this equation.

V=1.5(40)^2=2400m/s

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