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A rocket, initially at rest on the ground, accelerates straight upward with a constant acceleration of 29.4 . The rocket accelerates for a period of 10.0 before exhausting its fuel. The rocket continues its ascent until its motion is halted by gravity. The rocket then enters free fall.

Find the maximum height, , reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity of 9.810 .

Since the acceleration is constant i used the equation

y=y0+v0t+.5at^2
y0=0
v0t=0
What is acceleration?
would it be 9.81 or 29.4?

The acceleration while thrusting is +29.4 m/s^2. You can use your formula, as written, to compute the height y after 10 seconds. At that time, the acceleration becomes -9.81 m/s^2. The easiest way to compute how much higher it goes after that (delta y)is to take the velocity at t=10 s (Vm = 294 m/s), and assume that the kinetic energy KE gets converted to additional potential energy.
g*delta y = (1/2)Vm^2

ymax = y(10s) + delta y

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