1.1. A motorboat going downstream overcame a raft at point A; T=60 minutes later it turned back and after some time passed the raft at a distance l=6.0 km from the point A. Find the flow velocity assuming the duty of the engine to be constant.

1.2. A point traversed half the distance with a velocity V0. The remaining part of the distance was covered with velocity V1 for half the time, and velocity V2 for the other half of the time. Find the mean velocity of the point averaged over the whole time of motion.

1.3. A car starts moving rectilinearly, first with acceleration w=5.0 m/s^2 (the initial velocity is equal to zero), then uniformly, and finally, decelerating at the same rate w comes to a stop. The total time of motion T=25s. The average velocity during that time is <v> = 72 km per hour. How long does the car move uniformly?

1.4. (not done due to graph)

1.5. Two particles, 1 and 2, move with constant velocities v1 and v2. At the initial moment, their radius vectors are equal to r1 and r2. How must these four vectors be interrelated for the particles to collide?

1.6. A ship moves along the equator to the east with velocity v0=30km/hour. The southeastern wind blows at an angle a=60 degrees to the equator with velocity v=15 km/hour. Find the wind velocity v' relative to the ship and the angle a' between the equator and the wind direction in the reference frame fixed to the ship.

1.7. Two swimmers leave point A on one bank of the river to reach point B lying right across the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v0=2.0 km/hour and the velocity v' of each swimmer with respect to water equals 2.5 km per hour.

1.8 Two boats, A and B, move away from a buoy anchored at the middle of a river along the mutually perpendicular straight lines: the boat A along the river, and the boat B across the river. Having moved off an equal distance from the buoy, the boats returned. Find the ratio of times of motion of boats TA/TB if the velocity of each boat with respect to water is n=1.2 times greater than the stream, velocity.

1.9 A boat moves relative to water with a velocity which is n=2.0 times less than the river flow velocity. At what angle to the stream direction must the boat move to minimize drifting?

1.10 Two bodies were thrown simultaneously from the same point: one straight up, and the other, at an angle of a=60 degrees to the horizontal. The initial velocity of each body is equal to V0= 25 m/s. Neglecting the air drag, find the distance between the bodies t=1.70 s later.