Question

One of your friend challenged you to play basketball. The height of your friend is 2 m and he can do basket 3.5m away from pole. The height of basketball pole is 2.5m. You need to win from your friend. However, Your height is 1.5m.

(a) At which angle will you shoot basketball for basket?

Answer 1

Equation of the trajectory of a basketball

$y=x\tan\alpha-(1+\tan^2\alpha)\frac{gx^2}{2v_0^2}$

So,

$x=3.5(m)$ and $y=2.5-1.5=1(m)$

Assume that $v_0=10.5(m/s)$

$1=3.5\cdot\tan\alpha-(1+\tan^2\alpha)\frac{9.81\cdot 3.5^2}{2\cdot 10.5^2} \to$

$\alpha_1\approx25.5°$ or $\alpha_2\approx80.5°$