Help with Vectors: Calculating Displacement, Speed & Velocity

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In summary, the conversation discusses a problem where Darryl drives his truck loaded with tomatoes a certain distance in different directions and the time it takes. The problem asks to calculate his distance and displacement, and then his average speed and velocity. The solution is provided with calculations and a diagram, and the issue of displacement direction is addressed with a helpful link provided.
  • #1
jesstryin
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Homework Statement



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).

Homework Equations



sinb/b =sinC/C

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.
 
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  • #2
Hi jesstryin. Welcome to Physics Forums.

Your method looks right, though I haven't checked your arithmetic.
 
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  • #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!
 
  • #4
Your displacement magnitude calculation is correct.

Don't forget that vector quantities are specified by a magnitude and a direction.
 
  • #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!
 
  • #6
jesstryin said:
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.
I believe this link explains that.

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

FAQ: Help with Vectors: Calculating Displacement, Speed & Velocity

1. What are vectors and why are they important in science?

Vectors are mathematical quantities that have both magnitude (size) and direction. They are important in science because they help us describe and understand the movement of objects in the physical world. Vectors are used in a variety of fields, including physics, engineering, and navigation.

2. How do you calculate displacement using vectors?

Displacement is the change in position or location of an object. To calculate displacement using vectors, you need to determine the initial and final positions of the object and then find the difference between them. This can be done by subtracting the initial vector from the final vector.

3. What is the difference between speed and velocity?

Speed is the rate at which an object moves, while velocity is the rate at which an object moves in a specific direction. In other words, velocity takes into account the direction of movement, while speed does not.

4. How do you calculate speed using vectors?

To calculate speed using vectors, you need to divide the magnitude of the displacement vector by the time it takes for the object to travel that distance. This will give you the average speed of the object.

5. Can you have a negative displacement, speed, or velocity?

Yes, you can have negative displacement, speed, or velocity. This indicates that the object is moving in the opposite direction of the chosen reference point. For example, a car traveling south would have a negative displacement, speed, and velocity if the reference point is north.

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