Question

# 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 $$m/s^{2}$$)

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

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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