00:01
Hello students, in this question, we need to determine the values of r dot and theta dot, r dot and theta dot by using the details which are given in this figure.
00:18
Let a denote the car 1 and b denote the car 2, which are moving in the different paths.
00:28
This is one path and this is another path, moving in the opposite direction.
00:36
For car a, it is 75 meters from the origin, but for car b, it is 105 meter distance from the origin.
00:45
And they are traveling by making an angle of 5a, that is 45 degree and 5b, that is 30 degree, respectively, of car a and car b with the x axis.
01:02
First, here, let us write what are the things given in the figure.
01:09
5a is equal to 45 degree, 5b is equals to 30 degree, which is minus because in negative direction of y.
01:22
Hence from the cosine rule, that is r square is equal to r a square plus r b square minus 2 r a r b, cause of y a minus 5b, by a minus 5b.
01:39
By substituting the value of phi a, phi b and ra, rb, this is ra and this is rb, we get the value of r, that is 112 .12 .1320 meter.
01:59
Now to find theta, apply law of signs.
02:03
This is law of cosines.
02:05
Now apply law of signs.
02:06
That is sine of 90 minus theta divided by r a which is equals to sine of phi a minus 5b divided by r.
02:27
Therefore, sine of 90 minus theta divided by ra is 75 meters and sine of phi a is 45 and 5b is 30 by doing negative we get 75 because sine b is minus 30 divided by r or we have find that is 112 .132.
03:08
After calculating we get the theta value that is theta is equal to 49 .75 degree.
03:18
Now let us take the velocity which they have given for the car b that is b is equal to 30 km per hour.
03:30
If we convert this to meter per second we get 8 .33 meter per second and ba is equals to 40 kilometers per hour...