Determining Displacement Using Vector Components

[killaI9BI]

Homework Statement

This problem has had me puzzled for hours. I really appreciate any help you can provide.

A light plane leaves Shelburne, NS and flies 195km [N15°W] to Saint John, NB. After picking up a passenger, it flies to Moncton, NB which is 149km [N33°E]. The entire trip took 3.75h.

Calculate the average velocity of the plane for the entire trip from Shelburne, NS to Moncton, NB.

Homework Equations

a² + b² = c²
tan Θ = y-coordinates/x-coordinates

The Attempt at a Solution

d_sjx = (-195) X cos75 = (-50.47)km W
d_sjy = 195 X sin75 = 188.36km N
d_mx = 149 X cos57 = 81.15km E
d_my = 149 X sin57 = 124.96km N
d_x = (-50.47) + 81.15 = 30.68km E
d_y = 188.36 + 124.96 = 313.32km N

r² = 30.68² + 313.32²
r² = 99110.68
r = 314.8
314.8/3.75 = 83.95/h

tan θ = 313.32/30.68 = 10.21
θ = 84.4

The average velocity is 84km/h W 84 N.

The books answer is 48km/h [W29°N]

 

[haruspex]

I agree with your answer. I'd guess one of the given pieces of information has a wrongly stated compass direction, but I haven't been able to figure out exactly what. If these are real places, consult a map.

 

[killaI9BI]

Thank you. I did consult a map which says the distance between Shelburne NS and Moncton, NB is 262km which appears to be different than both mine and the books answers. I've double and triple checked the information provided and it's all accurate.

I'm doing grade 11 physics via correspondence with nobody to ask questions to. Questions like these sort of ruin my flow. Do you think I should submit this answer?

 

[olivermsun]

How do you interpret the heading W 84 N?

 

[haruspex]

Thank you. I did consult a map which says the distance between Shelburne NS and Moncton, NB is 262km which appears to be different than both mine and the books answers. I've double and triple checked the information provided and it's all accurate.

OK. The 33 degrees stated looks a bit low to me. Judging from Google maps it's more like 40 degrees, but that could be deceptive. Anyway, your answer is a lot closer to reality than the book answer. Submit it.

 

[killaI9BI]

How do you interpret the heading W 84 N?

Sorry for the delayed response

84 degrees North of West