HW#7 Ch 3: Vectors
1. The x component of vector \(\vec A\) is −2.25 m and the y component is +10.0 m. a) What is the magnitude of \(\vec A\) ? b) What is the angle between the direction of \(\vec A\) and the positive direction of x?
2. a) In unit-vector notation, what is the sum \(\vec A + \vec B\) if \(\vec A = \left( {4.0m} \right)\hat i + \left( {3.0m} \right)\hat j\) and \(\vec B = \left( { - 12.0m} \right)\hat i + \left( {5.0m} \right)\hat j\)? What are the b) magnitude and c) direction of \(\vec A + \vec B\) ?
3. In the space below or on your own paper, use a ruler to draw the vectors a) \(\vec A + \vec B\) and b) \(\vec A - \vec B\) graphically. Label each vector.
4. In the sum \(\vec A + \vec B = \vec C\), vector \(\vec A\) has a magnitude of 12.0 m and is angled 30.0° counterclockwise from the +x direction, and vector \(\vec C\) has a magnitude of 15.0 m and is angled 50.0° counterclockwise from the −x direction. What are a) the magnitude and b) the angle (relative to +x) of \(\vec B\)?
5. The stadium in the city of Bochum is 12.87 km east of the center of Essen. Starting from Essen, a VfL Bochum fan walks 12.41 km in a direction 15° south of east and then walks 4.71 km due north. How far is the fan then from the stadium?