Question

gimme idea newtons cannon

Answer 1

Hello, dan815,
"gimme idea" ? What happened to "Please give me some hints on how to solve a "Newton's Cannon" problem (see below)"

Answer 2

xD

Answer 3

xD
So Newton or somebody like him is standing on top a mountain 400 m above sea level. Is that it?

Answer 4

Wow, that'd be a very, very low flying satellite!

Answer 5

yeh

Answer 6

Let's get out of the way.

If the satellite really is revolving around the earth at an elevation of 400 m, then its velocity has two components: tangential and radial. Sound familiar?

Answer 7

right yes

Answer 8

so our tangential acceleration has to be constantly 0 if this satellite is indeed orbitting

Answer 9

what im trying to do is find a more like computational way of just finding given some time step, what the new position of the satellite is, what its new velocity vector looks like

Answer 10

and im not too sure how to apply the radial and tangential acceleration parts to find this changing velocity vector

Answer 11

the magnitude of the tangential component is given and is
\[A _{r}=\frac{ gmM }{ r ^{2} }\]

Answer 12

A=GmM/r^2

Answer 13

I'm not all that sure either. however, we're not defeated yet, are we, dan?
suppose that the straight line acceleration of a thrown particle is given as A. How would you obtain a formula for the velocity of this particle? Hint: think integration

Answer 14

okay heres a picture

Answer 15

Then, once y ou have a formula for velocity for this particle, how would you proceed to find a formula for the position of the particle? I am asking you these questions because doing so just might lead you to the solution of the problem you've posted.