I need some help with these two physics questions on vectors:
33. An ocean liner leaves New York City and travels 18.0° north of east for 155 km. How far east and how far north has it gone? In other words, what are the magnitudes of the components of the ship's displacement vector in the directions (a) due east and (b) due north?
The correct answer is (a) 147 km. (b) 47.9 km. I was wondering how did they get this result as the correct answer. Please show your work. Thanks.
5. As the earth rotates through one revolution, a person standing on the equator traces out a circular path whose radius is equal to the radius of the earth (6.38 X 106 m). What is the average speed of this person in (a) meters per second and (b) miles per hour?
The correct answer is (a) 464 m/s (b) 1040 mi/h. I was wondering how did they get this result as the correct answer. Please show your work. Thanks.
This solution both calculates the vector components and speed of the Earth in a step-by-step manner with full workings and diagrams for aid.