Question

Derive a equation for trajectory project tile
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Answer 1

Answer:

The horizontal component of velocity always remain same as there is no acceleration on the horizontal axis.

Thus, the horizontal distance travelled by the projectile is

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)

Where,

y is the horizontal component,

x is the vertical component,

g= gravity value,

v= initial velocity,

θ = angle of inclination of the initial velocity from horizontal axis.

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