Need help with vector question about calculating magnitude of total displacement

Question

On a bike ride you ride east at 10 miles/hour for 20 minutes then ride north at 11 miles/hour for 30 minutes and then ride southwest (45^o west of south) at 22 miles/hour for 15 minutes

Calculate the magnitude of your total displacement at the end of the ride.

I found the vectors for each x and y component and used the Pythagorean theorem and I still got the answer wrong. I got 2.17 miles.

Answer 1

d = speed (mi/hr) × time (hr)

Calculated Distances

10/3 mi E

11/2 mi N

22/4 mi SW = 11/2 mi SW which has components 

(11/(2√2)) mi S + (11/(2√2)) mi W

First find East-West and North-South displacements by simple subtraction.

Net East-West displacement

(11/2√2 – 10/3) mi W

Total North-South displacement

(11/2 – 11/(2√2)) mi N

Now use the Pythagorean Theorem to calculate the magnitude of total displacement.

Magnitude of total displacement

 √[(11/2√2 – 10/3)² + (11/2 – 11/(2√2))²] =

Calculate this and you'll come up with a number between 1 and 2.

Hope this helps! Just add a comment if you have any questions.