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 point will be

Question

Infinity Learn · Accepted Answer

As the horizontal ranges are the same.∴  $$v02sin2$$θ$$1g=v02sin2$$θ$$2gSo$$,  $$sin2$$θ$$1$$ $$=$$ $$sin2$$θ$$2or$$         $$2$$θ$$1$$ $$=$$ π $$-$$ $$2$$θ$$2$$⇒   θ$$1$$ $$+$$ θ$$2$$ $$=$$ π$$/2$$∴  $$h1max=v02sin2$$θ$$12gand$$  $$h2max=v02sin2$$θ$$22g$$∴  $$h1maxh2max=sin2$$θ$$1sin2$$θ$$2=sin2$$θ$$1cos2$$θ$$1=tan2$$θ$$1$$                                   ∵$$sin2$$θ$$2=sin2$$$$π$$$$2-$$θ$$1=cos2$$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 point will be

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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 point will be

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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 point will be