Question:
In a soccer practice session the football is kept at the center of the field 40 yards from the $10 \mathrm{ft}$ goalposts. A goal is attempted by kicking the football at a speed of $64 \mathrm{ft} / \mathrm{s}$ at an angle of $45^{\circ}$ to the horizontal. Will the ball reach the goal post?
Solution:
$y=x \tan \theta-\frac{1}{2} g \frac{x^{2}}{u^{2} \cos ^{2} \theta}$
$=(40 \times 3) \tan 45-\frac{1}{2} \frac{(32)(40 \times 3)^{2}}{(64)^{2}(\cos 45)^{2}}$
$=120-112.4$
$y=7.5 \mathrm{ft}<$ height of goalpost
So, football will reach the goalpost
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