An object is projected from the earth's surface with escape velocity at 3 0 ° with horizontal. What is the angle made by the velocity with horizontal when the object reaches a height 2 R from the

Question

An object is projected from the earth's surface with escape velocity at 3 0 ° with horizontal. What is the angle made by the velocity with horizontal when the object reaches a height 2 R from the earth's surface? R is the radius of the earth. Horizontal can be considered as a line parallel to the tangent at the earth's surface just below the object.

TestHub · Accepted Answer

- G M m R + 1 2 m x 2 G M R = - G M m 3 R + 1 2 m v 1 2 ⇒ v 1 = 2 G M 3 R By conservation of angular momentum: m × 2 G M R c o s 30 ° × R = m × v 1 c o s θ × 3 R ⇒ c o s θ = 1 2 ⇒ θ = 6 0 °

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