A small object is projected horizontally from the top of a tower of height $$40$$ m with a velocity of $$10$$ $$m/s$$. Simultaneously another small object is projected from the base of the tower with a velocity of $$20$$ $$m/s$$ making an angle θ with horizontal in the same plane. If the objects collide at a point at time t, find t.

Question

A small object is projected horizontally from the top of a tower of height $$40$$ m with a velocity of $$10$$ $$m/s$$. Simultaneously another small object is projected from the base of the tower with a velocity of $$20$$ $$m/s$$ making an angle  θ with horizontal in the same plane. If the objects collide at a point at time t, find t.

Infinity Learn · Accepted Answer

$$h1+h2=4012$$ $$gt2+usin$$θ.t−$$12$$ $$gt2=H$$⇒   $$t=Hu$$ $$sin$$θ$$=4020sin$$θ$$=2sin$$θAgain,  $$10$$ ×  $$t=20$$  $$cos$$θ ×  t ⇒  θ$$=600$$∴       $$t=2sin$$ $$600$$ $$=$$ $$43$$ $$sec$$

Projection Under uniform Acceleration

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Projection Under uniform Acceleration

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h1+h2=4012 gt2+usinθ.t−12 gt2=H⇒ t=Hu sinθ=4020sinθ=2sinθAgain, 10 × t=20 cosθ × t ⇒ θ=600∴ t=2sin 600 = 43 sec

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