a) Two identical pellet guns are fired simultaneously from the edge of a cliff.

Question

a) Two identical pellet guns are fired simultaneously from the edge of a cliff. These guns impart at an initial speed of 30.0 m/s to each pellet. Gun A is fired straight upward, with the pellet going up and then falling back down, eventually hitting the ground beneath the cliff. Gun B is fired straight downward. In the absence of air resistance, how long after pellet B hits the ground does pellet A hit the ground? (Just background info, answer to a is 6.12 sec) b) b. Sketch functions of both velocity and displacement versus time, for both pellets.

Explanation / Answer

Let: u be the firing speed of the gun, h be the height reached by pellet A above the clifftop, t be the required time difference, g be the acceleration due to gravity. When pellet A arrives back at the starting level, it has velocity u downwards. This is identical to the initial velocity of pellet B. The descent from the cliff therefore takes the same time for each pellet. The additional time required by pellet A is the time taken to ascend and return to the starting point. 0 = ut - gt^2 / 2 t(u - gt / 2) = 0 The non-zero root is: t = 2u / g = 2 * 30 / 9.81

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