In U.S. football, after a touchdown the team has the opportunity to earn one mor

Question

In U.S. football, after a touchdown the team has the opportunity to earn one more point by kicking the ball over the bar between the goal posts. The bar is 10.0 ftabove the ground, and the ball is kicked from ground level, 36.0 ft horizontally from the bar (the figure (Figure 1) ). Football regulations are stated in English units, but convert to SI units for this problem.

If the ball is kicked at 48? above the horizontal, what must its initial speed be if it to just clear the bar? Express your answer in m/s.

Explanation / Answer

To just clear the bar, in the horizontal direction, 36 ft converts to 10.97 m

In the horizontal d = vt

10.97 = v(cos 48)t

t = 10.97/v(cos 48) = 16.4/v (use that below)

In the vertical, d = vot + .5at^2

10 feet converts to 3.05 m

3.05 = v(sin 48)t + .5(-9.8)(t^2)

3.05 = vsin48(16.4/v) + (.5)(-9.8)(16.4^2/v^2)

3.05 = 12.2 - 1318/v^2

9.15 = 1318/v^2

v = 12 m/s

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