Question

Derive and solve the equation of motion of a particle, in a uniform gravita-

tional field, projected with initial horizontal velocity v 0 at a height h.

Answer 1

$v_x=v_0\cos \alpha,$

$v_y=v_0\sin \alpha-gt,$

$x=v_0\cos\alpha t,$

$y=y_0+v_0\sin\alpha t-\frac{gt^2}2,$

$y(x)=y_0+\tan\alpha x-\frac{gx^2}{2v_0^2\cos^2\alpha},$

$\alpha=0,$

$y_0=h,$

$y(x)=h-\frac{gx^2}{2v_0^2}.$