Question

a meteorite approaching a planet of mass M(in the straight line passing through the centre of the planet) collides with an automatic space station orbiting the planet in a circular trajectory of radius r. The mass of the station is ten times as large as the mass of meteorite. As a result of the collision, the meteorite sticks with the station which goes over to a new orbit with the minimum distance r/2 from the planet. Speed of the meteorite just before it collides with the space station is?

Answer 1

Let the mass of meterorite be m and initial velocity of station be u and velocity of the station+meterorite system be v.

Now since station moves in circular path.

a = u²/r

GM/r² = u²/r

u= √(GM/r)

since it is an inelastic collison and net external force equals zero
thus by conservation of linear momentum

10m * u + mV = 11m * v
V = 11v - 10u

now applying the centripetal acceleration after collison we get

v = √2GM/r

thus V = 11√(2GM/r) - 10√GM/r