The key to making a concise mathematical definition of escape velocity is to consider the energy. if an object is launched at its escape velocity, what is the total mechanical energy e_total of the object at a very large (i. e., infinite) distance from the planet follow the usual convention and take the gravitational potential energy to be zero at very large distances. consider the motion of an object between a point close to the planet and a point very far from the planet. indicate whether the following statements are true or false. angular momentum about the center of the planet is conserved. total mechanical energy is conserved.

An charge with mass m and charge q is emitted from the origin, (x,y)=(0,0). a large, flat screen is located at x=l. there is a target on the screen at y position y(h), where y(h) > 0. in this problem, you will examine two different ways that the charge might hit the target. ignore gravity in this problem. 1.assume that the charge is emitted with velocity v(0) in the positive x direction. between the origin and the screen, the charge travels through a constant electric field pointing in the positive y direction. what should the magnitude e of the electric field be if the charge is to hit the target on the screen? express your answer in terms of m, q, y(h), v(0), and l. 2.now assume that the charge is emitted with velocity v(0) in the positive y direction. between the origin and the screen, the charge travels through a constant electric field pointing in the positive x direction. what should the magnitude e of the electric field be if the charge is to hit the target on the screen? express your answer in terms of m, q, y(h), v(0), and l.

Using the free-body diagram, calculate the net force acting on the sled. is the sled in a state of dynamic equilibrium?

Which type of energy is transferred by convection currents?