00:01
Hi there, so for this problem, we have an athlete that starts at point a and runs at a constant speed of 7 meters per second around a round track that is 10 meters in diameter.
00:17
So it moves in this direction.
00:22
And then the diameter of this circular path is as 100 meters.
00:32
The radius of this is 50 meters, and it runs at a constant speed, and that constant speed is equal to 7 meters per second.
00:47
So the questions in here, well, for par a, par b, sorry, for par b, we are asked to find the white component of these runners average velocity between these points a and b.
01:00
Now, the first thing that we need to determine is the time for one full lap.
01:09
So the time for one full lap is equal to the perimeter of this, which is two times pi times the radius, and this divided by the velocity that we are given.
01:19
So that will be two times pi times 50 meters, and this divided by seven meters per second.
01:26
So from this, we obtain a value of 44 .88 seconds.
01:38
So because from a to b, it takes one quarter lap, then we need to divide this time by four.
01:48
So the time that it takes from a to b is one -fourth of the time that we determine.
01:57
So that will be 11 .22 seconds.
02:03
Now with that said, we can obtain the average white component of the velocity between the points a and b because that is going to be the position at a, the y position at a, which is, as you can see from here, zero.
02:26
So that will be, we go from zero to minus, the position of b.
02:36
So as you can see from the figure, oh, sorry, yes, well, sorry, is the final position, which is the position of b.
02:47
So as you can see from here, the white component of the position at b is corresponds to the radio, so that will be 50 meters minus the initial position at a, which is zero because it is along the white axis, has no altitude at that position, and this divided by the time that we determine, which is 11 .22 seconds.
03:11
So the average speed in the y direction is equal to a value of 4 .46 meters per second.
03:24
So that's the value for par b...