Two particles are projected upwards with the same initial velocity $$v0$$ in two different angles of projection such that their horizontal ranges are the same. The ratio of the heights of their highest points will be

Question

Infinity Learn · Accepted Answer

As the horizontal ranges are the same $$v02sin$$⁡$$2$$θ$$1g=v02sin$$⁡$$2$$θ$$2g$$ or  $$sin$$⁡$$2$$θ$$1=$$$$sin$$⁡$$2$$θ$$2$$ or  $$2$$θ$$1=$$π−$$2$$θ$$2$$  or  θ$$1+$$θ$$2=$$π$$/2$$ Now  $$h1max=v0sin$$⁡θ$$122g$$ and  $$h2max=v0sin$$⁡θ$$222g$$∴ $$h1maxh2max=$$$$sin$$⁡θ$$12sin$$⁡θ$$22=sin2$$⁡θ$$1cos2$$⁡θ$$1=tan2$$⁡θ$$1$$

Two particles are projected upwards with the same initial velocity v₀ in two different angles of projection such that their horizontal ranges are the same. The ratio of the heights of their highest points will be

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Two particles are projected upwards with the same initial velocity v0 in two different angles of projection such that their horizontal ranges are the same. The ratio of the heights of their highest points will be

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Ready to Test Your Skills?

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Two particles are projected upwards with the same initial velocity v₀ in two different angles of projection such that their horizontal ranges are the same. The ratio of the heights of their highest points will be