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An object is thrown horizontally from a point '$$A$$' from a tower and hits the ground $$3s$$ later at $$B$$. The line from '$$A$$' to '$$B$$' makes an angle of $$30^{\circ}$$ with the horizontal. The intial velocity of the object is :
(take g = 10 $$m/s^{2}$$)
292907_9f1cd9d13a6140ad88c48cc94f3c0017.png


A
153m/s
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B
15m/s
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C
103m/s
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D
253m/s
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Solution

The correct option is A $$15\sqrt{3}\, m/s$$
Object takes $$3s$$ to fall.
Hence AC = height $$ = \cfrac{1}{2} gt^{2} = \cfrac{1}{2} \times 10 \times 9 = 45m$$
Also:
$$tan 30^{\circ} = \cfrac{AC}{BC} = \cfrac{1}{\sqrt{3}}$$
$$BC = \sqrt{3} AC = 45\sqrt{3} m$$
The object covers AB in $$3s$$, hence initial velocity $$ = \cfrac{BC}{3} = 15\sqrt{3} ms^{-1}$$

Physics

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