Question

Derivation of projectile motion in detail

Answer 1

If these two motions are combined -vertical free fall motion and constanthorizontal motion - then the trajectory will be that of a parabola. An object which begins with an initial horizontalvelocity and is acted upon only by the force of gravity will follow the path of the blue sphere.x = u cosθ × t

 

t = x/(u cosθ)                                                   ...... (1)

 

The vertical distance travelled by projectile is given from kinematical equation s = ut + ½at2.

Here, s = y, a = ay = -g, u = uy = u sinθ

 

Thus, we have

 

y = u sinθ - ½gt2                                              ...... (2)

 

Substituting equation (1) in (2), we get

y=xtanθ−gx^2/2v^2cos^2(θ)