Solving the Last Practice Problem: A Coast Guard Challenge

[anuman]

I'm studying for an exam and can't seem to get this last practice problem! I've tried many ways but still keep getting the wrong answer. The professor has already given us the correct answer to the problems, but I want to know HOW to do it for the exam! Thanks in advance :)

A boat radioed a distress call to a Coast Guard station. At the time of the call, a vector A from the station to the boat had a magnitude of 45.0 km and was directed 15.0° east of north. A vector from the station to the point where the boat was later found is B = 30.0 km, 15.0° north of east.

12. What are the components of the vector from the point where the distress call was made to the point where the boat was found? In other words, what are the components of vector C = B - A?

x component y component
A)17.3 km, east 35.7 km, south
B)35.7 km, west 17.4 km, north
C)40.6 km, east 51.2 km, south
D)17.3 km, west 51.2 km, south
E)40.6 km, east 35.7 km, north

13. How far did the boat travel from the point where the distress call was made to the point where the boat was found? In other words, what is the magnitude of vector C?
A)65.3 km B)39.7 km C)26.5 km D)54.0 km E)42.5 km

 

[danago]

How did you attempt the problem?

Did you first resolve each of the given vectors into their two components?

You should show us your attempt at the problem so we can see where you may have gone wrong.

 

[anuman]

This is how I attempted it...I have been in the hospital for a while so I don't have class notes.

45sin15=11.64 30sin15=7.76
45cos15=43.46 30cos1515=28.97

11.64+7.76=19.4 y-component
43.46+28.97=72.43 x-component

 

[LowlyPion]

This is how I attempted it...I have been in the hospital for a while so I don't have class notes.

45sin15=11.64 30sin15=7.76
45cos15=43.46 30cos1515=28.97

11.64+7.76=19.4 y-component
43.46+28.97=72.43 x-component

Careful. Draw a diagram.

I don't think the terms combine in the way that you attempted.

The first vector is 15° to the right of North. This could also be written as 75° north of East if it would help you not to mix the Sines and Cosines.

Also you did a vector addition not a subtraction.

The easiest way to subtract is to add the inverse of the second vector.