Question

Erica is participating in a road race. The first part of the race is on a 5.2 mile long straight road oriented at an angle of 25 degrees north of east. The road then turns due north for another 6 miles to the finish line. In miles, what is the straight line distance from the starting point to the end of the race?

Answer 1

In first part of race displacement of Erica is

d1 = 5.2 mile at 25 deg North of East

x and y-component of 1st part of race will be:

d1 = 5.2*cos 25 deg i + 5.2*sin 25 deg j

d1 = (4.71 i + 2.20 j) miles

In second part of the race

d2 = 6 miles towards north, So

d2 = (6 j) miles

Now net displacement of Erica will be, Using Vector addition:

d = d1 + d2

d = (4.71 i + 2.20 j) + (6 j)

d = 4.71 i + 8.20 j

So Magnitude of net displacement will be:

|d| = sqrt (4.71^2 + 8.20^2)

|d| = 9.46 miles = distance between starting point and ending point