**P. 4491.** A spaceship is orbiting around the Earth. The distance between the spaceship and the surface of the Earth is the same as the radius of the Earth. Operating the rockets on the spaceship for a short time, the direction of the velocity of the spaceship is changed such that the angle between the actual radius drawn to the spaceship and the velocity is =150^{o}. The speed and the height of the spaceship above the Earth surface is unchanged.

*a*) By what amount will the spaceship go further away from the surface of the Earth?

*b*) Without altering again the path of the spaceship, at what speed would the spaceship hit the surface of the Earth?

(Neglect the effect of air and the rotation of the Earth.)

(5 points)

**P. 4494.** All the resistances of the resistors shown in the *figure* are *R*=2 M, the capacitance of the capacitor is *C*=1 F, the voltage of the battery is *U*=90 V. The switch *K* is held at its closed position in order to charge the capacitor, and then it is opened.

*a*) What is the reading on the ideal voltmeter before opening the switch?

*b*) What is the reading on the voltmeter a short time after the switch was opened?

(4 points)

**P. 4496.** A small object of mass *m* slides along a slope which is attached tangentially to a cart of mass *M*. In the middle of the cart a hemicylinder of radius *R* is attached to the cart as shown in the *figure.* The small object of mass *m *just reaches the top point *A* of this hemicylinder, stops there for an instant, then it falls freely and just hits the rim of the car. *a*) At least how long is the cart? *b*) What is the mass of the cart? *c*) From what height did the small object slide down? (*m*=2 kg, *R*=0.6 m. Friction is negligible everywhere.)A small object of mass *m* slides along a slope which is attached tangentially to a cart of mass *M*. In the middle of the cart a hemicylinder of radius *R* is attached to the cart as shown in the *figure.* The small object of mass *m *just reaches the top point *A* of this hemicylinder, stops there for an instant, then it falls freely and just hits the rim of the car.

*a*) At least how long is the cart?

*b*) What is the mass of the cart?

*c*) From what height did the small object slide down?

(*m*=2 kg, *R*=0.6 m. Friction is negligible everywhere.)

(6 points)