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Vertical Motion of a Rocket

Q: A rocket moves upward, starting from rest with an acceleration of 27.2 m/s2 for 3.49 s. It runs out of fuel at the end of the 3.49 s, but does not stop. How high does it rise above the ground?

A: Okay the rocket’s moving up with an acceleration of +27.2m/s^2 for a time of 3.49 seconds. It starts from rest, so we know Vi=0. We assume the rocket is leaving from Earth, so that would mean it also has downward acceleration of -9.8 m/s^2.

Write down what you know:
Vi = 0
a = 27.2 – 9.8 = 17.4
t = 3.49 seconds
d = ?

Find the Kinematics Equation that is needed to solve your question:

d = Vi*t + (1/2)at^2
d = 0*3.49 + 17.4/2 * (3.49)^2
d = 8.7(3.49^2)
d = 105.97
d = 106 metres