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

In summary, a harpsichordist has to drive 124 miles in 2.01 hours to get to a concert in time. His average speed is 63.7 mi/hr.
  • #1
slu1986
36
0
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.
 
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  • #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.
 
  • #3
Jebus_Chris said:
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.

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?
 
  • #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.
 
  • #5
Jebus_Chris said:
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.

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
 
  • #6
Could someone please help me understand how to work this problem?
 

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

1. What is the difference between average velocity and average speed?

Average velocity is a vector quantity that measures the displacement of an object over time, while average speed is a scalar quantity that measures the distance traveled over time. Average velocity takes into account the direction of motion, while average speed does not.

2. How do I calculate average velocity?

To calculate average velocity, divide the total displacement of an object by the total time taken for that displacement. The formula is: average velocity = total displacement / total time.

3. How is average speed different from instantaneous speed?

Average speed is calculated over a period of time, while instantaneous speed is the speed at a specific moment in time. Average speed takes into account any changes in speed during the time period, while instantaneous speed only measures the speed at that exact moment.

4. Why is it important to calculate average velocity and average speed?

Knowing the average velocity and average speed of an object can help us understand its overall motion and how it changes over time. It is especially useful in situations where an object's speed or direction may vary, such as in a car or airplane.

5. Can average velocity and average speed be the same?

Yes, if an object is moving in a straight line with a constant speed, its average velocity and average speed will be the same. This is because the object's displacement and distance traveled will be equal, and there will be no changes in direction to affect the average velocity.

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