Aproton is projected toward a fixed nucleus of charge +ze with velocity vo. initially the two particles are very far apart. when the proton is a distance r from the nucleus its velocity has decreased to 1/2vo.
how far from the nucleus will the proton be when its velocity has dropped to 1/4vo?
4/5 r
1/4 r
1/2 r
1/16 r

Astone weighing 1.5 kilograms is resting on a rock at a height of 20 meters above the ground. the stone rolls down 10 meters and comes to rest on a patch of moss. the gravitational potential energy of the stone on the moss is joules.

The field between two charged parallel plates is kept constant. if the two plates are brought closer together, the potential difference between the two plates either a) decrease b) does not change c) increase?

To place a communications satellite into a geosynchronous orbit at an altitude of 22,240 mi above the surface of the earth, the satellite first is released from a space shuttle , which is in a circular orbit at an altitude of 185 mi, and then is propelled by an upper-stage booster to its final altitude. as the satellite passes through a, the booster's motor is fired to insert the satellite into an elliptic transfer orbit. the booster is again fired at b to insert the satellite into a geosynchronous orbit. knowing that the second firing increases the speed of the satellite by 4810ft/s, determine (a.) the speed of the satellite as it approaches b on the elliptic transfer orbit, (b.) the increase in speed resulting from the first firing at a.