Phack...physics help?

[Sumguy]

Can't quite seem to understand whats going on in the problem.

"A projectile is shot directly away from the Earth's surface (neglect rotation). What multiple of Earth's radius gives the radial distance a projectile reaches if (1) its initial speed is .5 of the escape speed from Earth and (2) its initial kinetic energy is .5 of the kinetic energy required to escape Earth?"

For the problem KE=(1/2)mv^2 and potential energy is PE=-GMm/r

Escape velocity is sqrt(2GM/R)

R=Radius of the Earth
r=distance between Earth and rocket (center of masses)
G=gravitational constant
M=mass of Earth
m=mass of rocket

 

[Freshgeardude]

thats a little higher than my AP level of physics. have you tried to plug in, especially for escape velocity?

if its simpler than the wording and i am reading it as you are trying to find the maximum height:

find the escape velocity to make it 1) .5 of that speed and plug into 1/2mv^2 and to plug in for -GMm/r and solve for r (note mass cancels out and doesnt affect the outcome). and 2) use whole value found for escape velocity, plug in 1/2mv^2 and divide by two. use that answer and plug into -GMm/r

Ive been used to h as change in height, so I was confused at first, but since r is the variable being used at your level, go for it.

beyond that, im not sure. hope I helped

 

[dighn]

thats a little higher than my AP level of physics. have you tried to plug in, especially for escape velocity?

if its simpler than the wording and i am reading it as you are trying to find the maximum height:

find the escape velocity to make it 1) .5 of that speed and plug into 1/2mv^2 and to plug in for mgh ( mass x gravity x height) and solve for height (note mass cancels out and doesnt affect the outcome). and 2) use whole value found for escape velocity, plug in 1/2mv^2 and divide by two. use that answer and plug into mgh

beyond that, im not sure. hope I helped

essentially correct. just need to use the given equation for GPE instead of mgh (which is just an approximation for small scale distances on earth's surface.)

 

[Freshgeardude]

essentially correct. just need to use the given equation for GPE instead of mgh (which is just an approximation for small scale distances.)

yep, just realized r was being used in that equation for height. switched it

 

[drinkmorejava]

easy, just integrate the potential energy up to whatever the energy of the projectile is. Escape is 11200m/s without earth's rotation 107xx something with rotation. I'm guessing you're not doing any deltaV stuff with trajectories to maintain orbit.

actually, you don't even need to integrate here, just set KE=PE and solve for r

 

[El Guaraguao]

I cant personally define then term, "smart". Anybody on this planet can make up formulas and take for granted, that those formulas are legit and post them on random forums. I never took physics in school. For the simple fact that, I don't really want to become a astronaut or anything related in that field.

The reason I clicked on the OP thread, was to see if that person was devising a program to knock out THE 80ton asteroid, out of the direct path to a collision to earth.

 

[Sumguy]

Got it, basically set up initial mech. energy=final mech. energy and solved from there. Equation was KE (using v=.5 escape velocity) + GPE = GPE at a distance R+h. Hooray conservation of energy. Everything cancels out and you get h in terms of the radius of the Earth, which is what they apparently wanted. It moves a distance 1/3 R before stopping.

Basically a mix of what Freshgeardude and drinkmorejava said to do.