Mario, a hockey player, is skating due south at a speed of 4.79 m/s relative to the ice. a teammate passes the puck to him. the puck has a speed of 9.13 m/s and is moving in a direction of 17.8 ° west of south, relative to the ice. what are (a) the magnitude and (b) direction (relative to due south) of the puck's velocity, as observed by mario

Mario's velocity vector relative to the ice is

(note that all velocities mentioned here are given in m/s)

The puck is moving in a direction of 17.8 degrees west of south, or 252.2 degrees counterclockwise relative to east. Its velocity vector relative to the ice is then

The velocity of the puch relative to Mario is

Then, relative to Mario,

a. the puck is traveling at a speed of , and

b. is moving in a direction such that

which is about west of south.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.