Given in the picture attached below[/B]
The Attempt at a Solution
I had no idea how to tackle this problem.[/B]
I thought that V was inversely proportional to time. This led me to substitute (1/V) as T into Kepler’s Law.
If you can get the eccentricity and then find the slope at the latus rectum, I suppose you could go that route. It seems cumbersome to me. (although I'm absolutely willing to be shown otherwise).Gneill, is it not the case that, even after finding the tangent line to the ellipse at that point, one would need to use conservation of angular momentum to find the velocity at a later time? As such, I'm not sure saying it won't help is really accurate. There's just an intermediary step before finding the initial angular momentum.
Yes, I used the relationship a^2 - b^2 = c^2 for an ellipse, where a is semi major axis length, b is semi minor axis length, and c is focal length. I knew a and c, so I substituted and just solved for b^2. Using the Latus Rectum properties, b^2/a is the y-coordinate.
No idea what you actually did there. How did you find the slope of the ellipse? And with respect to what? You need to post details of your work if we're to help.I found the angle of the velocity to be 63.5 degrees, but when I solved using angular momentum I got a different answer. What I did to find the angle was set up the right triangle (between the two foci and the point), and use inverse tangent to find one of the angles, and use basic addition and manipulation of angles to figure out the rest.