Question

Explain Equation of Trajectory and derive it.

Answer 1

Trajectory formula is given by

 

y=xtanθ−gx22v2cos2θ

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,

Trajectory related equations are:

TimeofFlight:t=2v0sinθg

Maximumheightreached:H=20sin2θ2g

HorizontalRange:R=V20sin2θg

Where,
Vo is the initial Velocity,
sin θ is the y-axis vertical component,
cos θ is the x-axis horizontal component.

Answer 2

Trajectory means the path traced by a projectile.
Suppose a projectile of mass ‘m’ is projected with velocity ‘u’ at an angle θ with the ground.
The horizontal component of the initial velocity is, ux = u cosθ [this remains constant]

The horizontal displacement at any time ‘t’ is, X = ux×t = ut cosθ
=> t = X/(u cosθ)
The vertical component is given by, uy = u sinθ
The vertical displacement at any time ‘t’ is, 
Y=uyt−12gt2
=utsinθ−12gt2
or Y=u[X/ucosθ]sinθ−12g[X/(ucosθ)]2
Y=Xtanθ−gX2/[2u2cos2θ]