A particle is projected with a velocity u so that its horizontal range is twice the greatest height attained. The horizontal range $$is-$$

Question

Infinity Learn · Accepted Answer

Greatest height attained $$h=u2sin2$$θ$$2g$$                                                ....(1)                              Horizontal range $$R=u2sin$$⁡$$2$$θ$$g=2u2sin$$⁡θ$$cos$$⁡θ$$g---(2)$$ Given that $$R=2h$$⇒$$2u2sin$$⁡θ$$cos$$⁡θ$$g=2u2sin2$$⁡θ$$2g$$⇒$$tan$$⁡θ$$=2$$ Hence $$sin$$⁡θ$$=25$$;  $$cos$$⁡θ$$=15$$; substitute these values in $$equation(2)R=2u2sin$$⁡θ$$cos$$⁡θ$$gR=2u2(25)(15)gR=4u25g$$

A particle is projected with a velocity u so that its horizontal range is twice the greatest height attained. The horizontal range is-

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