A jogger travels due south and in the process his displacement vector has a magnitude of 4.68 km. he then jogs due west what is the magnitude of the displacement vector in the due west direction if the magnitude of the total displacement vector is 7.41 km

In this case, we can draw a right triangle. We are given the measure of one of the sides and the hypotenuse. Therefore we can calculate for the magnitude of the west direction using the hypotenuse formula. Let us say that b = west distance:

7.41^2 = b^2 + 4.68^2

b^2 = 33.0057 km^2

b = 5.75 km

Hence the magnitude in the west direction is about 5.75 km