problem 1.21

problem 1.20

problem 1.19

Part (when intial angular velocity is not zero)

problem: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. in book.Assuming the coordinate of the point x = 0 at the moment t = 0, draw the approximate time dependence plots for the acceleration w_x, the x coordinate, and the distance covered s.

problem 1.17

PROBLEM: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 I from the highway. It is known that the car moves in the field times slower than on the highway. At what distance from point D one must turn off the highway?

                                                                                  

problem 1.16

Two particles, 1 and 2, move with constant velocities v1 and v₂ along two mutually perpendicular straight lines toward the intersection point O. At the moment t = 0 the particles were located at the distances l1 and l₂ from the point 0. How soon will the distance between the particles become the smallest? What is it equal to?

problem 1.15

 A elevator car whose floor-to-ceiling distance is equal to 2.7 m starts ascending with constant acceleration 1.2 m/s²; 2.0 s after the start a bolt begins falling from the ceiling of the car. Find:

(a)   the bolt’s free fall time;

(b)   the displacement and the distance covered by the bolt during the free fall in the reference frame fixed to the elevator shaft.

problem 1.14

    A train of length I = 350 m starts moving rectilinearly with constant acceleration w = 3.0-10^-2 m/s²; t = 30 s after the start the locomotive headlight is switched on (event 1), and t = 60 s after that event the tail signal light is switched on (event 2). Find the distance between these events in the reference frames fixed to the train and to the Earth. How and at what constant velocity V rela­tive to the Earth must a certain reference frame K move for the two events to occur in it at the same point?

problem 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 At the initial moment of time v perpendicular to u and the points are separated by a distance L. How soon will the points converge?

problem 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 converge?

problem 1.11

Two particles move in a uniform gravitational field with an acceleration g. At the initial moment the particles were located at one point and moved with velocities v_x = 3.0 m/s and v₂ = 4.0 m/s horizontally in opposite directions. Find the distance between the particles at the moment when their velocity vectors become mutu­ally perpendicular.

problem 1.10

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

problem 1.9

problem 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 t_a/t_b if the velocity of each boat with respect to water is r) = 1.2 times greater than the stream velocity.

problem 1.7

Two swimmers leave point A on one bank of the river to reach point B lying right across on 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.

problem 1.6

problem 1.5

    problem1.5

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.

                                             

Problem 1.4

                                                          problem 1.4

A point moves rectilinearly in one direction as  Fig. 1.1 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 to at which the instantaneous velocity is equal to the mean velocity averaged over the first to seconds.