Question

On a beautiful day you decide to go for a bicycle ride. First you ride for 10 miles at 30 degrees south of east and then for 8.0 miles at 60 degrees north of west. What is the magnitude of your displacement?  

options:

a	12.7 mi
b	0
c	4.8 mi
d	15.5 mi
e	18 mi

Answer 1

Suppose given that Vector is R and it makes angle with +x-axis, then it's components are given by:

Rx = R*cos

Ry = R*sin

Now we need to find A + B

Using above rule:

A = 10 miles, 30 deg South of east (4th quadrant x > 0 & y < 0)

Ax = 10*cos 30 deg = 8.66 mi

Ay = -10*sin 30 deg = -5 mi

B = 8.0 miles, 60 deg North of west (2nd quadrant x < 0 & y < 0)

Bx = -8*cos 60 deg = -4 mi

By = 8*sin 60 deg = 6.93 mi

Now displacement will be

C = A + B

C = (Ax + Bx) i + (Ay + By) j

C = (8.66 - 4.0) i + (-5 + 6.93) j

C = 4.66 i + 1.93 j

So Magnitude of C will be

|C| = sqrt (Rx^2 + Ry^2)

|C| = sqrt (4.66^2 + (1.93)^2)

|C| = 5.04 mi

None of the given options are correct, either discuss this issue with your TA, OR you can choose closest option C 4.8 mi. Please do not leave negative rating unless you mention error in my solution.