Answer to Question #185246 in Classical Mechanics for Petra

Question

You drive 7.50km in a straight line in a direction 15 degrees east of north.

A.) Find the distances you would have to drive straight east and than straight north to arrive at the same point. (This determination is equivalent to find the components of the displacement along the east to north directions).

B.) Show that you still arrive at the same point if the east and north legs are reversed in order. Give a sketch and show in equation form.

Answer 1

a)

$$S_{E}=7.5\sin{15}=1.94\ km\\ S_{N }=7.5\cos{15}=7.24\ km$$

b)

$$\bold{S=S_E+S_N=S_N+S_E}$$

If the east and north legs are reversed in order, the total route will be A –D –B instead of A –C –B. As it can be seen from the diagram, the resulting displacement will be still equal to AB.