# Final Displacement

1. A cyclist rides 3.0 km due west, then 16.0 km 23° west of north. From this point she rides 9.0 km due east. What is the final displacement from where the cyclist started (in km)? (Express your answer in vector form. Assume the +x-axis is to the east, and the +y-axis is to the north.)

Picture of question: https://gyazo.com/31eff7abeed1f8ef80293518c12f183b

2. Displacement = r final - r initial

3. I converted the cardinal coordinates to (3, 180 degrees), (16, 113 degrees), and (9,0 degrees). The total of the vectors in vector form is -0.25i + 14.7j. That's the displacement if the origin is (0,0) by my estimation, but that answer was rejected. What am I missing?

verty
Homework Helper
Try 14.73 for the ##\hat{j}## component. Otherwise I get the same answers.

Austin Gibson
PeroK
Homework Helper
Gold Member
2021 Award
1. A cyclist rides 3.0 km due west, then 16.0 km 23° west of north. From this point she rides 9.0 km due east. What is the final displacement from where the cyclist started (in km)? (Express your answer in vector form. Assume the +x-axis is to the east, and the +y-axis is to the north.)

Picture of question: https://gyazo.com/31eff7abeed1f8ef80293518c12f183b

2. Displacement = r final - r initial

3. I converted the cardinal coordinates to (3, 180 degrees), (16, 113 degrees), and (9,0 degrees). The total of the vectors in vector form is -0.25i + 14.7j. That's the displacement if the origin is (0,0) by my estimation, but that answer was rejected. What am I missing?