Question

You travel 20 miles north and then 20 miles at 30 degrees north due east. What is your final displacement?

a) 20 miles
b) 30 miles
c) 40 miles
d) 50 miles

Answer 1

The final displacement is 40 miles.

Step-by-step explanation:

To find the final displacement, we need to find the components of each leg of the journey and then add them up. The north leg is simply 20 miles directly north, so its displacement is 20 miles north. The east leg can be divided into a north component and an east component. The north component is 20 * sin(30) miles, and the east component is 20 * cos(30) miles. Adding these components together, the east leg has a displacement of 10 miles north and 17.32 miles east. Now we can add the north and east displacements together using the Pythagorean theorem: sqrt((20 + 10)^2 + 17.32^2) = 40 miles. Therefore, the final displacement is 40 miles. Therefore, the correct answer is c) 40 miles.