Training Olimpiade Fisika Problem 1 30

Training 1: Problems

1.1 – 1.30

1.1. A motorboat going downstream overcame a raft at a point A; σ = 60 min later it turned

back and after some time passed the raft at a distance l = 6.0 km from the point A.

1.2. A point traversed half the distance with a velocity v_o. The remaining part of the

distance was covered with velocity v for half the time, and with velocity v for the other half of the time. Find the mean velocity of the

1.3. A car starts moving rectilinearly, first with

acceleration ω = 5.0 m/s2 (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 equals σ = 25 s. The average velocity during that time is

1.4. A point moves rectilinearly in one direction. Fig. 1.1 shows the distance s traversed by the point as a function of the time t.

Using the plot find:

(a) the average velocity of the point during the time of motion;

(b) the maximum velocity;

(c) the time moment t_o at which the

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

1.6. A ship moves along the equator to the east with velocity v_o = 30 km/hour. The

southeastern wind blows at an angle φ = 600 to the equator with velocity v = 15 km/hour.

1.7. Two swimmers leave point A on one bank of destination simultaneously? The stream velocity v_o = - 2.0 km/hour and the velocity v’ of each

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:

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

1.10. Two bodies were thrown simultaneously from the same point: one, straight up, and the other, at an angle of θ = 60 ° to the

1.12. Three points are located at the vertices of an equilateral triangle whose side equals a. They all start moving simultaneously with velocity v constant in modulus, with the first point heading continually for the second,

the second for the third, and the third for the first. How soon will the points

1.13. Point A moves uniformly with velocity v so that the vector v is continually "aimed" at point B which in its turn moves rectilinearly and uniformly with velocity u < v. At the

1.17. From point A located on a highway (Fig. 1.2) one has to get by car as soon as possible to point B located in the field at a distance l

from the highway. It is known that the car moves in the field η times slower than on

1.18. A point travels along the x axis with a

velocity whose projection v_x is presented as a function of time by the plot in Fig. 1.3.

Assuming the coordinate of the point x = 0 at the moment t = 0, draw the approximate time dependence plots for the acceleration ω_x, the x coordinate, and the distance

An equilateral triangle is move in such a way that point A moves with velocity v₀

toward point B and point C moves from point B, as shown in the figure.

Determine the velocity of point B.