**P. 4029.** A 2 kg body, moving on a frictionless horizontal track, reaches another object of 3 kg made of the same material, moving in front of the 2-kg object, and collides with it totally inelastically. Their common speed after the collision is 4 m/s. Due to the collision the temperature of the two objects, which was initially the same, is increased, though only by 0.006 ^{o}C. The specific heat capacities of the two objects are the same: .

*a*) What were the initial speeds of the colliding objects before the collision?

*b*) What percent of the initial kinetic energy is transferred to increase of the internal energy of the two objects?

(4 points)

**P. 4030.** A house, situated 100 m to the South of a straight road running East--West, contains a television set which is receiving signals from a distant transmitter, also situated South of the road, operating at a frequency of 60 MHz. A bus, travelling along the road in a westerly direction, causes the received signal to fluctuate in intensity, the rate of fluctuation is 2 Hz when the bus is opposite the house and (temporarily) reduces to zero when it is 200 m further along the road. Find the speed of the bus and the direction of the transmitter.

(5 points)

**P. 4031.** A positron of speed , collides with an electron which was initially at rest, and they annihilate. One of the created photon travels perpendicularly to the original direction of the velocity of the positron.

*a*) In what direction is the other photon emitted?

*b*) What is the ratio of the energies of the two photons?

(5 points)