t06 ⊾ ⊿ Name:

  1. θ = __________ The images show a sun dog to the left of the sun. The cloud that the sun is lighting up from behind is 50 kilometers away from me. The sun dog is 20.21 kilometers to the left the sun. Calculate the angle θ in degrees at which the sun dog forms.
    sun dog sun dog sun dog Right triangle θ 50 20.21
  2. Right triangle θ 13.68 15.8 θ = __________ For the fourth throw Iumileen measured a distance of 13 meters horizontally and Jamori read a stopwatch time of 0.95 seconds for a speed of 13.68 m/s horizontally. The speed of the ball along the ball's flight arc was 15.8 m/s. Use the diagram to solve for the angle θ.
  3. ____________ Calculate the magnitude of the vector v = 20i + 21j.
  4. ____________ Calculate the direction angle of the vector v = 20i + 21j when in standard position.
  5. 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:
    w⇀=3.9i towards Malem and my board was moving at
    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.
    1. Calculate my velocity v over the reef by adding the vectors w + s and reporting the magnitude of the resulting vector v: __________
    2. __________ Calculate the angle between the total velocity vector v and wave velocity vector w.
  6. Do NOT try at home: children towing a RipStik with a bicycle
    Do NOT try at home: Child towing a RipStik with a bicycle     __________ My daughter towed my son on a RipStik with a force of 100 Newtons at an angle of 30° to the horizontal for a distance of 40 meters. Calculate the energy (work done) using the dot product for this example.
  7. __________ 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 0.9 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. The experiment proved very dangerous and was not repeated.
  8. The bicycle provides a force of 100 Newtons at an angle of 30° to the horizontal. The RipStik generates a drag of 87 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.
    SVG trigonometry problems θ = 30° 100 87
  9. distance d = 2 v 2 sin⁡(θ) cos⁡(θ) 9.8 The equation for a ball arc is shown on the right. If Lane can throw the ball at 10 m/s, what angle θ will yield the most distance? Note that 2 × 100 ÷ 9.8 = 20.41 and that the equation uses x for θ.

    Make a plot of 20.41 sin(x) cos(x) to try to determine the angle x that produces the greatest distance d.
    1. x = ______________
    2. θ = _____________° If you plotted using Wolframalpha, then the solution x is probably in radians. What is the angle θ in degrees for that maximum distance?