1. Homework Statement
Attached in the picture below.Homework Equations
Spring energy = 0.5Kx2
Kinetic energy = 0.5mv2
The Attempt at a Solution
I tried setting the equations for spring energy and kinetic energy equal, since I thought the maximum compression would occur when the box had no...
What I did was that I considered the top angle of the triangle. Theta = arctan (a/0.75a) = 53.1 degrees. Then, the remaining two angles must add up to 180 - 53.1 = 126.9 degrees. Since they are the same, 126.9/2 = 63.4 degrees. Am I doing something wrong?
That was the conjugate angle. The angle in the triangle I got was a little more than 50 degrees. I then used the fact that the other two angles were equal, and that all the angles added up to 180 degrees (since they form a line) to get the angle of 63.5 degrees.
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.
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...
I am preparing for the U.S. Physics Olympiad exam currently. This is one of the problems from the F=ma exam, which is the preliminary test for USPHAO. https://www.aapt.org/physicsteam/2018/
As for finding the angle theta, wouldn’t that always be 90 degrees because the velocity is tangent to the ellipse? Also, I am not familiar with eccentricity or perihelion radius, so would there be any way to solve this?