Two particles are projected in air with speed u at angles θ$$1$$ and θ$$2(both$$ $$acute)$$ to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then which one of the following is correct?

Question

Two particles are projected in air with speed u at angles θ$$1$$ and θ$$2(both$$ $$acute)$$ to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then which one of the following is correct?

Infinity Learn · Accepted Answer

Height H $$=$$ $$u2sin2$$θ$$2gFor$$ the same speedH ∝ $$sin2$$ θ∵ $$H1$$ > $$H2$$ (Given)∴  $$sin2$$θ$$1$$  > $$sin2$$θ$$2or$$ θ$$1$$ > θ$$2----------(i)Time$$ of flight, T $$=$$ $$2u$$ $$sin$$θgFor the same speedT  ∝$$sin$$ θθ$$1$$ > θ$$2$$   (From$$ $$(i))∴   $$sin$$ θ$$1$$ > $$sin$$ θ$$2$$ ⇒ $$T1$$ > $$T2$$

Two particles are projected in air with speed u at angles $θ_{1} a n d θ_{2}$ (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then which one of the following is correct?

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Two particles are projected in air with speed u at angles θ1 and θ2(both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then which one of the following is correct?

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Two particles are projected in air with speed u at angles $θ_{1} a n d θ_{2}$ (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then which one of the following is correct?