An asteroid of mass m is approaching earth, initially at a distance 10 R e with speed v i . It hite oarth with a speed v f , R e and M e are radius and mass of earth ) , then

Step-by-step solution

Initial energy of the asteroid is E i = K i + U i = 1 2 m v i 2 - G M θ m 10 R e Final energy of the asteroid, E f = 1 2 m v f 2 - G M θ m R θ According to law of conservation of energy, E i = E f 1 2 m v i 2 - G M θ m 10 R θ = 1 2 m v f 2 - G M θ m R θ v f 2 - 2 G M θ R θ = v i 2 - 2 G M θ 10 R θ ⇒   v f 2 = v i 2 + 2 G M θ R θ 1 - 1 10