the initial horizontal speed be and the initial vertical speed be . It will also be shown that the range is , and the maximum altitude is . The maximum range for a given initial speed is obtained when , i.e. the initial angle is 45. This range is , and the maximum altitude at the maximum range is .

Derivation of the equation of motion

Assume the motion of the projectile is being measured from a free fall frame which happens to be at (x,y) = (0,0)

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