Calculate the final velocity of an object accelerating towards a mass

  • #1
I need to be able to calculate the final velocity of an object accelerating towards a mass from a distnce with an initial velocity. From my little knowledge of calculus, im only a junior in high school, i have figured out that this is probably a derivitive problem. But i have no knowledge of how to solve these kinds of equations. If im right would some one please walk me through it step-by-step. If i'm wrong, please correct me and show me how to do it step by step. This is not a homework problem but a problem i made up to challenge myself. The problem is i think im in way over my head. So any help would be amazing. Thanks
 

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  • #2
bapowell
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No, I think all you need here is to apply conservation of energy,

[tex]\Delta KE = -\Delta PE[/tex],

where PE is the gravitational potential energy between the two objects.
 
  • #3


But since acceleration due to gravity increases as the distance between the two objects decreases, you cant use PE=massxgravityxheight since the acceleration is constantly changing for a given height. or does that not matter? I worked it out and i got that an object of mass one kilogram starting from rest at a distnce of 3.8x10^8 meters would be traveling at 1450 m/s at the point of impact, disregarding air resistance.
 
  • #4
bapowell
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But since acceleration due to gravity increases as the distance between the two objects decreases, you cant use PE=massxgravityxheight since the acceleration is constantly changing for a given height. or does that not matter? I worked it out and i got that an object of mass one kilogram starting from rest at a distnce of 3.8x10^8 meters would be traveling at 1450 m/s at the point of impact, disregarding air resistance.
Right, you can't use [tex]PE = mgh[/tex]. Use Newton's Law of Gravitation.
 
  • #5
Janus
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But since acceleration due to gravity increases as the distance between the two objects decreases, you cant use PE=massxgravityxheight since the acceleration is constantly changing for a given height. or does that not matter? I worked it out and i got that an object of mass one kilogram starting from rest at a distnce of 3.8x10^8 meters would be traveling at 1450 m/s at the point of impact, disregarding air resistance.
No you can't. you have to use

[tex]PE = -\frac{GMm}{r}[/tex]

Where r is the distance between the centers of m and M.

Just remember that [itex]\Delta PE[/itex] is the difference in PE between the start of the fall and the end of the fall.
 

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