**P. 4371.** A pebble shot by a slingshot has an initial vertical, upward speed of 50 m/s. If there was no air drag

*a*) where would the pebble be after 7 seconds;

*b*) What would its speed be at that moment;

*c*) How much distance would it cover in 7 seconds?

(3 points)

**P. 4373.** Bodies of mass *m*=0.5 kg, resting on a horizontal frictionless tabletop, are connected with an unstretched spring of length *L*=20 cm, and of spring constant *D*=16 N/m. The mass of the spring is negligible. At a certain moment the bodies are given an initial speed of *v*_{0}=0.36 m/s, towards the wall on the right. The body at the right collides with the wall totally elastically.

*a*) What is the greatest compression of the spring during the motion?

*b*) After the collision with the wall how much time elapses until the moment when the bodies are the closest?

*c*) Will there be any other collision with the wall later? How will the system of bodies move if a long enough time elapses? *d*) What is the change in the linear momentum of the system after all collisions occurred?

(4 points)

**P. 4376.** Two capacitors of capacitances *C*_{1}=180 pF and *C*_{2}=20 pF were connected in series, and their free terminals were connected to the terminals of a rechargeable battery which could supply a constant e.m.f. of *U*_{0}=24 V. (The dielectric between the plates of both condensers was air.) Thus in both capacitors some energy was stored. Later the energy stored in the condensers was increased, with the same amount in both. This was done by filling totally the space between the plates of the capacitor of capacitance *C*_{2} by glass, the relative dielectric constant of which is _{r}. The connection of the capacitors and the other capacitor of capacitance *C*_{1} were not changed.

*a*) What was the relative dielectric constant _{r} of the glass which was used?

*b*) By what amount did the energy of the condensers increase? (The relative dielectric constant of air is 1.)

(5 points)