Question

With what velocity must a body be thrown upward from the surface of the earth so that it reaches a height of 10R ? Earth's mass equal to 6 x 10^24 kg, radius of earth equal to 6.4x10^6 m and G equal to 6.67 x 10^-11N-m^2/kg^2.

Answer 1

Dear Student,

◆ Answer -

v = 10679 m/s

● Explanation -

For body to reach certain height, kinetic energy equals to work done by the body.

Kinetic energy = Work done

1/2 mv^2 = GMm [(1/R - 1/(R+h)]

v^2 = 2GM × h / [R(R+h)]

Substitute h = 10R,

v^2 = 2GM × 10R / [R(R+10R)]

v^2 = 20GM/11R

As GM/R = gR,

v^2 = 20gR/11

v^2 = 20 × 9.8 × 6.4×10^6 / 11

v^2 = 1.14×10^8

v = 10679 m/s

Hence, body must be thrown at velocity of 10679 m/s.

Thanks dear. Hope this helps you...