A meteorite of mass m= 2×10^4 kg is approaching head-on a planet of mass M= 4×10^29 kg and radius R= 2×10^4 km. Assume that the meteorite is initially at a very large distance from the planet where it has a speed v0= 5×10^2 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=
The potential energy of the meteorite is approximately GMm/distance.
Add that PE, and the initial KE of the meteorite, and that is the final KE of the body, 1/2 mv^2, solve for v.
What is the distance here?
My bob that approach got me a wrong answer. :(
Yes, this method is not working
try PE=0 as its at infinity
5*10^5 m/s ???
Well, think a little... If you're at an infinity distance, your gravitational potential must be zero, as you see: -mMG/distance, if distance is infinity, it doesn't metter -mMG as somehow it is some constant. So, you have some velocity at "infinity" so you have some kinect energy, (m * v0^2)/2... So you see, conservation says that Potential_A + Kinect_A must be equal to Potential_B + Kinect_B, so at B, it will be when you hit the planet... Well, now you're not anymore at some infinity distance, so you have some potential energy, from the distance of the center of the planet, that distance is R, then you have -mMG/R, and now you have some Kinect energy, m * v1^2/2, this v1^2 is the "collision" velocity. So, all you must do now, is put v1 at evidence, then you have something like this: m*v0^2/2 = -mMG/R + m*v1^2/2; cut down those "m", you have v0^2/2 = -MG/R + v1^2/2; put v1^2 at evidence "throwing" -MG/R to the otherside, you have: v1^2/2 = v0^2/2 + MG/R; "throw" 2 to the otherside: v1^2 = v0^2 (you don't need 2 here, cause it's already divided by 2) + 2MG/R; Almost there now, now you take the square root of it: v1 = sqrt(v0^2 + 2MG/R). So, now you have it. Just remember, at infinity, potential energy is zero, and remember to convert those values. I guess you'll get something like v1 = 1.708x10^6. I hope it helps. Good luck.
The formula for the meteorite problem is:
KE(initial)=KE(final) - GMm/(Radius of Earth)
Can somebody please help with the aeroplane landing and Pendulum problems? :(
hi buddies, for the airplane:
physicsforums com showthread.php?t=720405
I've worked out the pendulum and will post the solution as soon as i wake up now i need sleep, we have still 2 days left so no worries