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Kicking a field goal y EXAMPLE 3.6 For a field goal attempt, a football is kicked from a point on the Uo = 20.0 m/s ground that is a horizontal distance S from the goalpost. For the 3.05 m attempt to be successful, the ball must clear the crossbar, 10 ft To 30.0° X (about 3.05 m) above the ground, as shown in Figure 3.18. The ball leaves the kicker's foot with an initial speed of o d 20.0 m/s at an angle of 30° above the horizontal. What is the dis- d2 tance d between kicker and goalpost if the ball barely clears the The ball can pass over the goalposts on the way up or crossbar? on the way down, so there are two possible values EXAMPLE 3.7 Robin Hood shoots a pear In a festival competition, the great archer Robin Hood is challenged to hit a falling pear with an arrow. At the sound of a horn, he is to shoot his arrow, and at the same instant the pear will be dropped from the top of a tall tower. As shown in Figure 3.19, Robin Hood aims directly at the initial position of the pear, seem- rivals ingly assume that this is a mistake, but to their shock, he hits the pear. Show that if the arrow is location aimed directly initial making no allowance for the fact that the pear is dropping as the arrow moves toward it. His at the initial position of the pear, it will always hit the pear, regardless of the pear's initial or speed (assuming that neither pear nor arrow hits the ground first). y Line of sight to pear Path of pear ? Notice tan00 = " I'm Does the arrow that hit the pear? Trajectory of arrow To x On S A FIGURE 3.19 Robin Hood's shot.

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