An object is vertically thrown from ground The position of t

An object is vertically thrown from ground. The position of the object is 20 m below relative to the origin of the coordinates. Find followings u_x, u_y, x, and y (each variable as a function of time t. Find the trajectory equation.

Solution

As per the given co-ordinates initial position of ball (0,-20).

Assume angle of projection with respect to ground is .

Lets also assume initial velocity with which ball is thrown is V.

Now Vx₀ = V cos ; Vy₀ = V sin

Acceleration in vertical direction = -g

Distance travelled in time t in horizontal direction = V cos *t (where t – time of travel)

Distance travelled in time t in vertical direction = V sin * t- ½*g*t²

To get the trajectory equation we can solve by replacing t = X_t /VCos from Eqn 1 in in Eqn 2,thus