Help with Vectors: Calculating Displacement, Speed & Velocity

[jesstryin]

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.

 

[NascentOxygen]

Hi jesstryin. Welcome to Physics Forums.

Your method looks right, though I haven't checked your arithmetic.

 

[jesstryin]

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!

 

[NascentOxygen]

Your displacement magnitude calculation is correct.

Don't forget that vector quantities are specified by a magnitude and a direction.

 

[jesstryin]

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!

 

[NascentOxygen]

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