Question

A projectile is given an initial velocity of 5 m/s at an angle 30° below horizontal from the top of a building 25 m high. Find (a) the time after which it hits the ground; (b) the distance from the building where it strikes the ground. (g = 10 m/s²)

Moderate

Solution

The projectile is thrown from point O and lands at point A on the ground.
From O to A : s_y = -25m, u_y = -5 sin30^o = -2.5m / s (negative because vertical component acts downwards)
$(a) We have a_{y} = - g = - 10 m / s^{2} \begin{array}{l} s_{y} = u_{y} t + (1 / 2) a_{y} t^{2} \\ - 25 = - 2 .5 t - (1 / 2) (10) t^{2} \end{array}$
So, therefore 10t² + 5t - 50 = 0. On solving, we get is t = 2s, -2.5 s.
The relevant time is 2s.
$(b) s_{x} = u_{x} t = (5 \cos 30^{\circ}) 2 = 5 \sqrt{3} m .$

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