Derive an expression for the gravitational potential energy U(r) of the object-earth system as a function of the object's distance from the center of the earth. Take the potential energy to be zero when the object is at the center of the earth.

Determine the maximum r-value of the polar equation r =3+3 cos 0

Arunner is training for an upcoming marathon by running around a 100-m-diameter circular track at constant speed. let a coordinate system have its origin at the center of the circle with the x-axis pointing east and the y-axis north. the runner starts at (x, y) = (50 m, 0 m) and runs 2.5 times around the track in a clockwise direction.

What are the north and south poles of a solenoid change with?