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Word problem: Asking to solve for average velocity and average speed

  1. Sep 6, 2009 #1
    1. 1. To get to a concert in time, a harpsichordist has to drive 124 miles in 2.01 hours.

    (a) If he drove at an average speed of 53.0 mi/h in a due west direction for the first 1.18 h, what must be his average speed if he is heading 30.0° south of west for the remaining 49.8 min?

    (b) What is his average velocity for the entire trip?

    2. Equations:

    avg velocity = Δr/Δt
    avg speed = distance traveled/time of trip


    3. I am confused at how to calculate average speed in this problem..do you take the -cos (30.0) 53.0 mi = -45.8 mi for the x component and sin (30.0) 53.0 mi = 26.0 mi for the y component and plug them into the pythagorean theorum = -45.8 mi^2 + 26.0 mi ^2 = 2799.89 mi and take the square root which is = 52.9 mi and divide that by .83 hrs = 63.7 mi/hr b/c 49.8 min is = 0.83 hr Am I doing this wrong? I'm not sure how to calculate the average velocity for this problem. Could someone please explain what I am doing wrong b/c the whole 30 degree angle in the problem throws me off.
     
  2. jcsd
  3. Sep 6, 2009 #2
    Draw a triangle. You have two vectors, one going west and the other going at 30 degrees south of west. You know the first vector and you also know the resultant so with that you can figure out the rest.
     
  4. Sep 7, 2009 #3
    I don't understand what vector value that I'm using the 30 degrees to solve for? Am I using it to get the resultant time or miles/hr? Do I take 53 mi/hr and divide that by .83 hrs and plug that answer in with the sin and cosine of 30.0 degrees to get the x and y components and then plug those into the pythagorean theorum?
     
  5. Sep 7, 2009 #4
    You don't know the value of the 30 vector, you have to find that out. You know what the resultant vector is. So if you add the components of the first two vectors you get the resultant vector.
     
  6. Sep 8, 2009 #5
    124 mi/2.01 hrs = 61.7 mi/hr
    53.0 mi/0.83 hr =63.8 mi/hr

    So would I add 61.7 mi/hr^2 + 63.8 mi/hr^2 = 7877.33 mi/hr and take the square root of this to get = 88.7 mi/hr?

    I'm confused..could you explain to me exactly what vectors you are talking about when you say add the two vectors to get the resultant vector
     
  7. Sep 8, 2009 #6
    Could someone please help me understand how to work this problem?
     
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