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Help with vectors?

  1. Mar 11, 2014 #1
    1. The problem statement, all variables and given/known data

    Hi everyone, my problem is this:

    Darryl drives his load of tomatoes 14.0 km [E], 6.0 km [N], 12.0 km [ N 15° E], and then 2.0 km [N 65° E]. This takes him 42 minutes.

    a) Calculate Darryl's distance and displacement. Draw a diagram and show your work.
    b) Calculate Darryl's average speed and average velocity (record your answer in m/s).

    2. Relevant equations

    sinb/b =sinC/C

    3. The attempt at a solution

    A. 14 km + 6.0 km + 12.0 km + 2.0 km = 34 km
    Total Distance is 34 km = 34,000 m

    D (east) = 14 + 12 * sin15 + 2 * sin65 = 18.9 km

    D (north) = 6 + 12 * cos15 + 2 * cos65 = 18.4 km

    C2 =√ a2 + b2
    D = √(18.9km² + 18.4km²)
    = 26.4 km

    My problem is that I think I miscalculated the displacement (east), for the speed and velocity calculation I did this:

    B.
    Vav (speed) = 34km / 42 min = 34,000 m / 2520 s
    Vav= 13.49 or 13.5 m/s


    Vav = 26.4 km / 42 min = 26,400 / 2520
    Vav (velocity) = 10.47 or 10.5 m/s

    I just need clarification for displacement, so that I can accurately calculate the velocity.
     
  2. jcsd
  3. Mar 11, 2014 #2

    NascentOxygen

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    Staff: Mentor

    Hi jesstryin. Welcome to Physics Forums.

    Your method looks right, though I haven't checked your arithmetic.
     
  4. Mar 11, 2014 #3
    Thank you! Could you let me know if I got the answer correct for displacement, I feel like I'm missing a step and need the displacement to calculate the right velocity. Thanks so much!
     
  5. Mar 11, 2014 #4

    NascentOxygen

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    Staff: Mentor

    Your displacement magnitude calculation is correct.

    Don't forget that vector quantities are specified by a magnitude and a direction.
     
  6. Mar 11, 2014 #5
    So, is the answer for displacement 26.4 km N 54.9 degrees E ? Or is it 26.4 km E 54.9 degrees N ? I think it is the former, but I am not sure.

    Thank you for all the help I appreciate it!
     
  7. Mar 11, 2014 #6

    NascentOxygen

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    Staff: Mentor

    I believe this link explains that.

    http://www.compassdude.com/compass-units.shtml
     
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