Homework Statement
A boy is seated on the top of a hemispherical mound of ice. He is given a very small push and starts sliding down the ice. Show that he leaves the ice at a point whose height is 2R/3 if the ice is frictionless. (Hint:The normal force vanishes as he leaves the ice.)...
Homework Statement
A rocket is accelerated to speed v=2√gR (where R is the radius of Earth 6370 km) near Earth's surface surface and it then coasts upward. a) show that it wil escape from Earth. b) Show that very far from Earth its speed will be v=2√gR.
Homework Equations
Gravitational...
Homework Statement
The fastest possible rate of rotation of a planet is that for which the gravitational force on material at the equator just barely proved the centripetal force needed for the rotation. a) show that the corresponding shortest period of rotation is
T=(√3π)/(√Gp)
where p...
Hey guys. I got a book that has selected problems/questions the from Russian/Soviet Math Olympics. Anyhow, I'm having trouble with a particular question that involves a quartic equation that, up to my knowledge, can't be factored. I was wondering if there are any tips or methods to solve for...
Thank you for the much appreciated feedback.
I guess I should have ask, how is each one different? And what are other advantages and disadvantages that have not already been mentioned in this thread?
Also, I have been reading similar threads regarding my question, and basically it comes...
Hey guys. Seeing that the Calculus textbooks of Apostol and Spivak have been mentioned and recommended numerous times in this forum, I was wondering which one is better?
Currently, I am senior taking calculus. I feel that my calculus class is too easy and will not help me in college where I...
Homework Statement
A rectangle is bounded by the x-axis and the semicircle y=√(36-x^2) (see figure). Write the area A of the rectangle as a function of x.
I will try to explain the figure as best as possible. The figure is basically a semicircle on the Cartesian plane with a domain of...