t06 ⊾ 13 July 2012 ⊿ Name:

1. ____________ Calculate the magnitude of the vector v = 8i + 15j.
2. ____________ Calculate the direction angle of the vector v = 8i + 15j when in standard position.
3. ____________ Calculate the magnitude (vector length) for the vector {80, 80}. Note that in the diagram on the above right all vectors are in the standard position with their initial point at the origin (0, 0).
   
4. ____________ Calculate the angle relative to the horizontal axis for the vector {80, 80}.
5. v = ______________________ Write the vector {80, 80} in i, j form.
6. ____________ Calculate the magnitude for the vector {−86.61, 50}.
7. ____________ Calculate the angle relative to the positive horizontal x axis for the vector {−86.61, 50}.
8. On a Thursday evening in July 2005 I was body board surfing in Malem. My total velocity v (speed) was the result of the vector addition of the velocity (speed) of the wave w and the velocity s of my board along the face of the wave. On that Thursday the waves were moving at a speed of:
   $\stackrel{\rightharpoonup }{w}=3.9i$ towards Malem and my board was moving at
   $\stackrel{\rightharpoonup }{s}=5.2j$ towards Lelu. Speed are in meters per second.
   Note that w and s are at right angles as shown in the inset diagram.
   
   Calculate my velocity v over the reef by adding the vectors w + s and reporting the magnitude of the resulting vector v: __________
9. __________ Calculate the angle between the total velocity vector v and wave velocity vector w.
10. 
    Do NOT try at home: Child towing a RipStik with a bicycle __________ My son is towing my daughter with a force of 100 Newtons at an angle of 30° to the horizontal for a distance of 20 meters. Calculate the energy (work done) using the dot product for this example.
11. __________ My son is towing my daughter with a force of 100 Newtons at an angle of 30° to the horizontal. The length of the lever arm d for the torque is 0.8 meters (the distance from the nose of the RipStik to the rear wheel). Calculate the torque on the RipStik using the cross product for this example.
    No children were injured in the production of this question. The actual attachment point for the rope was altered for the purposes of this problem.
12. The bicycle provides a force of 100 Newtons at an angle of 30° to the horizontal. The RipStik generates a drag of 40 Newtons at an angle of 180° to the horizontal. What is the direction angle and magnitude of the net force on the RipStik? Add the two vectors to determine the resulting direction angle and magnitude of the net force.