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Homework Statement
A 7500-kg rocket blasts off vertically from the launch pad with a constant upward acceleration of 2.25 m/s^2 and feels no appreciable air resistance. When it has reached a height of 525 m, its engines suddenly fail so that the only force acting on it is now gravity.
(a) What is the maximum height this rocket will reach above the launch pad?
Homework Equations
[itex]velocity_{y-axis} = v_{0y} + \int \! a_y \, \, dt[/itex]
[itex]position (y) = y_0 + \int \! v_y \, \, dt[/itex]
The Attempt at a Solution
First I list all the given information,
[itex]a_y = 2.25 m/s^2[/itex]
[itex]-g = -9.80 m/s^2[/itex]
Next I integrate [itex]a_y[/itex] in order to obtain the velocity,
[itex]v_y = \int \! 2.25 m/s^2 \, \, dt[/itex]
[itex]v_y = 2.25t[/itex]
Now I integrate [itex]v_y[/itex] in order to obtain the position,
[itex]y = \int \! 2.25t \, \, dt[/itex]
[itex]y = 1.125t^2[/itex]
And this is where I get confused. I solve the following quadratic equation in order to determine the maximum height that was reached (gravity gets differentiated, no?):
[itex]0 = 1.125t^2 -4.90t + 525[/itex]
And then I get 525.258 m instead of the correct answer of 646 m. What am I doing wrong?