Question

two particles a and b are projected from ground with same speed and at angles of projection 38° and 52° respectively with the horizontal. the horizontal range of motion will be​

Answer 1

horizontal range of particles will be same.

two particles a and b are projected from ground with same speed (let u) and at angles of projection 38° and 52° respectively.

we know horizontal range, R = u²sin2θ/g

horizontal range of particle, A = u²sin2(38°)/g = u²sin76°/g.....(1)

horizontal range of particle, B = u²sin2(52°)/g = u²sin104°/g

= u²sin(180° - 76°)/g

= u²sin76°/g......(2) [ as we know, sin(180° - θ) = sinθ]

from equations (1) and (2),

we get, horizontal range of particle ,A = horizontal range of particle , B

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Answer 2

The horizontal ranges are same.

Explanation:

Horizontal range is given by the formula:

R = (u₁²sin 2θ)/g

Particle a ⇒ u₁ = u and θ = 38°

R₁ = (u²sin 2(38))/g

∴ R₁ = (u²sin 76)/g

Particle b ⇒ u₁ = u and θ = 52°

R₂ = (u₁²sin 2(52))/g = (u₁²sin 104)/g

R₂ = (u₁²sin (180 - 76))/g

∵ sin (180 - x) = sin x

∴ R₂ = (u₁²sin 76)/g

From R₁ and R₂, we get,

∴ R₁ = R₂