What is your Displacement?

While visiting England, you decide to take a jog and find yourself in the neighborhood shown on the map shown in the figure.

What is your displacement after running 2.5 km on Strawberry Fields,1.7 km on Penny Lane, and 5 km on Abbey Road? 

First get the x & y

y = 5 cos(40) = 3.83

x = 5 sin(40) = 3.21

Our additional components from strawberry fields and penny laneare:
x_strawberry = 2.5km
y_penny = -1.7 km

Add your components to find the total of each direction.
x_total= 3.21 + 2.5 = 5.71

y_total = 3.83 – 1.7 = 2.13

To find displacement, use Pythagorean theorem.

d² = x² + y²

√5.71² + 2.13²

√32.6 + 4.53

= 6.1 km