Question

A Football player kicks a ball at an angle of ${30}^o$ to the horizontal with an initial velocity of $15m{s}^{-1}$. Assuming the ball travels in a vertical plane, Calculate the

a] Maximum height

b] Time of flight and

c] Horizontal range $[g=9.8m{s}^{-2}]$.

Answer 1

Angle of projection $\theta ={30}^0$

initial velocity, $\mu =15$ m/sec

a) Maximum height $=\frac{{\mu }^2{\sin }^2\theta }{2g}$

$=\frac{{\left(15\right)}^2\times {\sin }^2{30}^0}{2\times 9.8}$

$=2.869$ m

b) Time of flight for projectile $=\frac{2\mu \sin \theta }{g}$

$=\frac{2\times 15\times \sin {30}^0}{9.8}$

$=1.53$ sec

c) Range $=\frac{{\mu }^2\sin 2\theta }{g}$

$=\frac{{\left(15\right)}^2\times \sin {60}^0}{9.8}=\frac{225}{9.8}\times \frac{\sqrt{3}}{2}$

$=19.74$ m