Question

1. A projectile is released with a speed u at an angle θ to the horizontal. With the aid of a diagram, show that the time of flight is equal to 2u sinθ / g, where g is the acceleration of free fall.

Accepted Answer

For a projectile, the vertical component of velocity is uᵧ = u sinθ. From Newton's equation of motion, v = u + gt (free fall), taking g as negative for upward motion: v = uᵧ − gt (i). At maximum height, v = 0, so 0 = uᵧ − gt, giving t = uᵧ/g = u sinθ / g — this is the time to reach maximum height. Since the projectile's trajectory is symmetrical, it takes the same time to complete the rest of the flight, so the total time of flight T = 2 × (time to reach maximum height) = 2u sinθ / g.

WAEC Physics 2013 Theory — Question 1

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