Kicking a field goal
For a field goal attempt, a football is kicked from a point on the
ground that is a horizontal distance S from the goalpost. For the
attempt to be successful, the ball must clear the crossbar, 10 ft
(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
20.0 m/s at an angle of 30° above the horizontal. What is the dis-
tance d between kicker and goalpost if the ball barely clears the
The ball can pass over the goalposts on the way up or
on the way down, so there are two possible values
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).
Line of sight to pear
Path of pear
Notice tan00 = " I'm
Does the arrow
hit the pear?
Trajectory of arrow
FIGURE 3.19 Robin Hood's shot.
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