Question

A meteorite of mass m= 2 ×104 kg is approaching head-on a planet of mass M= 7 ×1029 kg and radius R= 5 ×104 km. Assume that the meteorite is initially at a very large distance from the planet where it has a speed v0= 5 ×102 km/s. Take G= 6.67 ×10−11.

Determine the speed of the meteorite v (in m/s) just before it hits the surface of the planet. (The planet has no atmosphere, so we can neglect all friction before impact)

v=

Answer 1

Intiial PE=GMm/r
Initial KE=1/2 m v^2
can you convert that intial energy to final ke?

Answer 2

my final formula is: Vf=sqrt(Vi^2+(mMG/r))
r being the radius of the planet

Answer 3

1/2 m vf^2=1/2 m vi^2+GMm/r

where r is the initial distance of the object. You can ignore the final PE, as the object is very far from the planet initiually. That does not lead to what you got.

Answer 4

but isn't the object initially at r=infinity therefore P_i=0 and the potential energy just before impact Mmg/the radius of the planet? or am i completely of target

Answer 5

1/2 m vf^2=1/2 m vi^2+GMm/r - it's correct!