Question

two particles are projected with same speed in different directions in the same vertical plane.both particles have same range. if their time of flights are 10 sec and 20 sec ,then range is(g=10).

Answer 1

I hope my answer will help you

Answer 2

Let the common speed of the both the Particles be u m/s.

Since, they both having the same range,

∴ R₁ = R₂

⇒ u²Sin2θ₁/g = u²Sin2θ₂/g

⇒ Sin2θ₁ = Sin2θ₂

║θ₁ + θ₂ = 90║

Now,

T₁ = 2uSinθ₁/g

T₂ = 2uSinθ₂/g

⇒ 10/20 = Sinθ₁/Sinθ₂

Sinθ₂ = 2 Sinθ₁

Sin(90 - θ₁) = 2Sinθ₁

Cosθ₁ = 2Sinθ₁

⇒ tanθ₁ = 1/2

⇒ θ₁ = tan⁻¹(1/2)

Sinθ₁ = 1/√5 and Cosθ₁ =2/√5

∴ Range = u²Sin2θ₁/g

⇒ Range = u² × 2/√5 × 1/√5/10

∴ Range = u²/25

Since, Initial velocity is not given, answer will be in its terms.

Hope it helps.