The equations of motion of a projectile are given by x=36 t metre and 2y=96t-9.8t²

The equations of motion of a projectile are given by x=36 t metre and 2y=96t-9.8t² metre. The angle of projection is

(a) sin⁻¹ (4/5)
(b) sin⁻¹ (3/5)
(c) sin⁻¹ (4/3)
(d) sin⁻¹ (3/4)

sin⁻¹ (4/5)

x = 36t ⇒ dx/dt = 36

.·. vₓ = 36 m/s and 2y = 96t – 9.8t²

⇒ y = 48t – 9.8 t² ⇒ dy/dt = 48 – 9.8t

.·. vᵧ = 48 – 9.8t

At t = 0

⇒ vᵧ = 48

.·. tan θ = vᵧ / vₓ = 48 / 36 = 4 / 3

⇒ sin θ = 4/5 ⇒ θ = sin⁻¹ (4/5)

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