Question

2. The horizontal component of the initial speed of a particle projected at 30° to the horizontal is 50 ms⁻¹. If the acceleration of free fall due to gravity is 10ms⁻², determine its: (a) initial speed; (b) speed at maximum height reached.

Accepted Answer

Given: uₓ = horizontal component of initial speed = 50m/s, angle of projection θ = 30°, g = 10m/s.
(a) uₓ = u cosθ, so u = uₓ/cosθ = 50/cos30° = 57.7 ms⁻¹.

(b) At maximum height, the vertical component of velocity vᵧ = 0. However, the final speed v at maximum height is not zero, because the horizontal component uₓ is still non-zero (there is no acceleration due to gravity acting horizontally, so gₓ = 0, meaning vₓ = uₓ). Using v² = uₓ² + vᵧ² = uₓ² + 0, so v = uₓ = 50 ms⁻¹. Speed at maximum height = 50 ms⁻¹.

WAEC Physics 2013 Theory — Question 2

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