A particle is fired vertically from Earth's surface with speed kvₑ, where vₑ is Earth's escape speed and k

Question

A particle is fired vertically from Earth's surface with speed kvₑ, where vₑ is Earth's escape speed and k < 1. Neglect air resistance and let Earth's radius be Rₑ. Find the maximum height h above the surface.

Options

G1 Physics · Accepted Answer

Initial energy is (1/2)m(kvₑ)² - GMm/Rₑ. At maximum height Rₑ+h, speed is zero. Using vₑ² = 2GM/Rₑ givₑ -GMm(1-k²)/Rₑ = -GMm/(Rₑ+h). Thus Rₑ+h = Rₑ/(1-k²), so h = Rₑk²/(1-k²). Correct answer: A.

A particle is fired vertically from Earth's surface with speed kvₑ, where vₑ is Earth's escape speed and k &lt; 1. Neglect air resistance and let Earth's radius be Rₑ. Find the maximum height h above the surface.

A particle is fired vertically from Earth's surface with speed kvₑ, where vₑ is Earth's escape speed and k < 1. Neglect air resistance and let Earth's radius be Rₑ. Find the maximum height h above the surface.