Quick Physics Question?

Question

A rocket moves upward, starting from rest with an acceleration of 30 m/s2 for 2.5 seconds. It runs out of fuel at the end of the 2.5 seconds but doesn't stop. How high does it rise above the ground?

Answer 1

The first leg of this flight is the acceleration phase
v(2.5)=30*2.5 call this v0
and
y(2.5)=15*2.5^2, call this y0

for t>2.5
v(t)=v0-g*t
when it reaches apogee, v(t)=0, solve for t
and
y(t)=y0+v0*t-.5*g*t^2
plug in the t from apogee and you get the height.

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