Velocity: Let us consider v_x and v_y are the horizontal and vertical component of velocities at point P(x, y). As gravitational acceleration (g) acts downwards, then horizontal component of acceleration is gcos90⁰ = 0.

So, v_x = u_x = ucos ——–(1)

And v_y = u_y – gt = usin – gt ——–(2)

So, the magnitude of velocity of particle at point P is v = ——–(3)

Displacement: Let us consider, the coordinates of point P is (x, y).

So, x = u_xt = utcos ——–(4)

And y = u_yt – gt² = utsin – gt² ——-(5)

The trajectory of the motion is y = usin() – g()²

 y = xtan – g()² ——–(6) This is the equation of parabola.

Maximum height: At point A, particle is at maximum height. At point A, the velocity of the particle is along the tangent. So, v_y= 0.

Therefore, usin – gt = 0 [using equation (2)]

∴ t =

Substituting the value of t in equation (5) we get, maximum height

H = usin() – g()²

∴ H =  ——— (7)

Time of flight: The total time taken by the particle during its motion is T. During time of flight then the net displacement along y axis is 0. From equation(5) we get, uTsin – gT² = 0

∴T =   ——–(8)

Range: The maximum horizontal distance travelled by the body is called range.

Range R = u_xT = ucos(  ) = .