Uniform Motion Review - Boat travelling

[anneku]

Homework Statement

A boat travelling close to the coast is heading in
an unknown direction. The captain contacts an
observer on the shore to help her determine the
direction the boat is heading. The observer on the
shore reports that the horizontal displacement of the
boat is 750 m [E] and that the boat travelled north
an unknown distance. The captain has measured a
total distance of 1100 m that the boat moved. How far
north did the boat travel and in what direction is the
boat travelling?

Relevant Equations

total displacement = change in position on x axis + change in position on y axis

displacement (x) = 750 m [E]
distance = 1100 m

I drew a diagram. Now what??

 

[phinds]

Homework Statement: A boat traveling close to the coast is heading in
an unknown direction. The captain contacts an
observer on the shore to help her determine the
direction the boat is heading. The observer on the
shore reports that the horizontal displacement of the
boat is 750 m [E] and that the boat traveled north
an unknown distance. The captain has measured a
total distance of 1100 m that the boat moved. How far
north did the boat travel and in what direction is the
boat travelling?
Homework Equations: total displacement = change in position on x-axis + change in position on y axis

displacement (x) = 750 m [E]
distance = 1100 m

I drew a diagram. Now what??

Show your work. You have the wrong answer.

 

[anneku]

Show your work. You have the wrong answer.

I got the correct answer as the displacement on the y-axis is 805 m [N] as this is a right-angled triangle (using Pythagorean theorem). The boat is also traveling [ E 47 N ] as cosΘ =750/1100 and therefore the angle would be 47°.

Why would the length of the hypotenuse be 1100 m though? 1100m is distance. It would be wrong to assume that the distance and displacement are the same.

 

[haruspex]

Show your work. You have the wrong answer.

Anneku did not quote an answer, merely restated the given data.

 

[haruspex]

Why would the length of the hypotenuse be 1100 m though? 1100m is distance. It would be wrong to assume that the distance and displacement are the same.

It does not say they are the same, and they cannot be because displacement is a vector.
There is an assumption that the direction is constant, so the distance traveled is the magnitude of the displacement.

 

[phinds]

Anneku did not quote an answer, merely restated the given data.

Ah. You're right. I missed that (obviously).