# Projectile: Mental Food - From the point of side of a hill two bodies are projected in the same vertical plane .......?

From the point of side of a hill two bodies are projected in the same vertical plane through the line of greatest slope.with the same velocity; but in directions at right angles to each other. Show that "The difference of their ranges is independent of their angles of projection.

billrussell42

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In a hill, value of slope varies from point to point. We have considered the line of greatest slope. Two bodies are projected in the vertical plane passing through this line with the same velocity but in directions at right angles to each other. All the angles refer to the Horizontal direction.

### 6 Answers

- Pramod KumarLv 72 months ago
Let the directions of Projection of the Particles be making angles, α₁ and α₂ respectively with the Horizontal Plane. One particle will go up the hill while the other will come downwards. Let their common velocity be u . And the slope of the hill = β

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- FiremanLv 72 months ago
as Range of a projectile (R) = u^2sin2θ/g, let the two projectile are θ and θ + 90* with the same initial velocity u,

=>R1 = u^2sinθ/g ------------------(i)

& R2 = u^2sin{2 x (θ + 90*)}/g

=>R2 = u^2sin(180* + 2θ)/g

=>R2 = u^2sin2θ/g ---------------(ii) {as sin (180* + 2θ) = sin2θ}

By (i) & (ii):

=>R1 = R2

- billrussell42Lv 72 months ago
unclear. what is "line of greatest slope" ?

"at right angles to each other" ? in what plane?

"angles of projection" angle with respect to what?

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