An American football quarterback stands at A. At the instant the quarterback thr

Question

An American football quarterback stands at A. At the instant the quarterback throws the football, the receiver is at B running at 20 ft/s toward C, where he catches the ball. The ball is thrown at an angle of 45 degrees above the horizontal, and it is thrown and caught at the same height above the ground. Determine the magnitude of the ball' initial velocity and the length of time it is in the air.

Explanation / Answer

yC=yA+V0y t-gt2/2 (note that yA = yC) => V0y = gt/2=16.1 t ft/s => Vsin45o = 16.1 t (2) For the ball horizontal motion V0x = Vcos45o SAC = V0xt = Vcos45o t (3) Use (1) in (3) v[302+(20t)2] = V cos45o t (4) Solving (2) and (4), we have V = 38.02 ft/s and t = 1.67 s

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