A body is projected downwards at an angle of $30^{0}$ to the horizontal with a velocity of 9.8 m/sec from the top of a tower 29.4 m high. How long will it take before striking the ground?
(g=9.9 m/s²)

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answer is B.

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Detailed Solution

$\begin{array}{l} g i v e n i n i t i a l v e l o c i t y = u = 9.8 m / s; d o w n w a r d a n g l e o f p r o j e c t i o n w r t h o r i z o n t a l = θ = 30^{0}; t o w e r h e i g h t = h = 29.4 m; g = 9.8 m / s^{2} \\ v e r t i c a l c o m p o n e n t o f t h e v e l o c i t y = v_{y} = U \sin θ = 9.8 \sin 30^{\circ}; T a k i n g d o w n w a r d a s + y - a x i s : \\ v_{y} = 4.9 m / \sec \\ We know h = U \sin θ t + \frac{1}{2} g t^{2}; s u b s t i t u t e g i v e n v a l u e s, \\ \Rightarrow 29.4 = 4.9 t + \frac{1}{2} (9.8) t^{2} \\ \Rightarrow t = 2 s e c = t i m e t a k e n t o s t r i k e t h e g r o u n d \end{array}$