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:
$\mathrm{y}=\mathrm{x} \tan \theta-\frac{1}{2} \mathrm{~g} \frac{\mathrm{x}^{\mathrm{2}}}{\mathrm{u}^{2} \cos ^{2} \mathrm{e}}$
$=(40 \times 3) \tan 45^{-\frac{1}{2}} \frac{(32)(40 \times 3)^{2}}{(64)^{9}(\cos 45)^{2}}$
$=120-112.4$
$y=7.5 \mathrm{ft}<$ height of goalpost
So, football will reach the goalpost