How do you find the distance a ball travels if fired at speed u and angle theta from the ground?
From a right angled triangle with hypotenuse u and angle theta, we see the horizontal speed is (u cos theta) and the initial vertical speed is (u sin theta). As the ball moves in a symmetric parabola, it hits the ground with vertical speed (-u sin theta).Therefore, the ball must be in the air for (2 u sin theta / g) seconds, so it travels a distance of (2 u^2 sin theta cos theta / g). This can be simplified to (u^2 sin (2 theta) / g).
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