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With what muzzle speed must a projectile be fired vertically from a gun on the surface of the Earth if it is to (barely) reach the distance of the Moon? Neglect the gravity of the Moon, neglect atmospheric friction, and neglect the rotational velocity of the Earth in the following problem. I am totally clueless as to how to approach the problem. i tried -GMm/r=1/2mv^2 but the answer is not correct.

Physics
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you need to use the kinematic equations to find the speed necessary to lift a bullet so that it "just" makes it to the moon before falling back down again. try using\[\Delta x = v_0 *t + \frac{1}{2} g*t^2\]\[(v_f)^2 = (v_0)^2 + 2a \Delta x\] and\or \[\Delta x = \frac{1}{2} (v_0 + v_f)*t\] I'd start with the second one, if I were you.
@JFraser How can I use equations of motion when the value of g is not constant.
assume that it is

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Other answers:

Wrong. I used Initial P.E + Initial K.E=Final K.E(which is zero) + Final P.E. Now the answer matches the back of the book.

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