Question

A rocket is fired upward from ground level with an initial velocity of 1600ft/sec . When will the rocket be above 1000ft? Show your work. Round your answer to the nearest tenths. Write the answer in set notation.

Answer 1

{t: 0.6 < t < 99.4}.

Explanation:

Use one of the equations of motion under gravity.

s = ut + 0.5gt^2 where s = distance, u = initial velocity, g = acceleration due to gravity and t = the time.

So we have:

1000 = 1600t + 0.5* -32*t^2 ( acc due to gravity is negative as we are acting against it).

16t^2 - 1600t + 1000 = 0

t = (1660 +/- sqrt(1600^2 - 4*16*1000) / 32

This gives t = 0.629 , 99.371 seconds.

So the time is above 0.6 seconds (to the nearest tenth) and before 99.4 seconds.