Question

You drive 14.00 km in a straight line in a direction 41° east of north. Find the distance you would have to drive straight east and then straight north to arrive at the same point. (This determination is equivalent to find the components of the displacement along the east and north directions.)

Answer 1

Answer:

9.1848 km straight east and 10.5659 km straight north

Explanation:

To find these distances, you just have to find the components of this displacement. The inclination in relation to north is 41 degrees, so to find the north component, you need to multiply 14 km by the cossine of 41 degrees, which is 0.7547.

So, the north component is 14 * 0.7547 = 10.5659 km

To find the east component, you multiply 14 by the sine of 41 degrees, which is 0.6561:

14 * 0.6561 = 9.1848 km

You would need to drive 9.1848 km straight east and then 10.5659 km straight north to arrive at the same point.