Wrong Answer in Textbook for Collision Velocity Calculation

[mafagafo]

Homework Statement

(Problem about a collision) (...). What then is their velocity in (a) unit-vector notation and as (b) magnitude and (c) angle.

I will not post the problem due to copyright issues and that it is absolutely pointless now.

The Attempt at a Solution

I was able to solve (a) and (b).
However, my answer for (c) differs from that of the textbook.
$$\text{a)} \;(2.67 \;\text{m/s})\hat{i}+(-3.00 \;\text{m/s})\hat{j}$$
$$\text{b)} \;4.01 \;\text{m/s}$$
$$\text{c)} \;\theta{} = \tan^{-1}\left(-\frac{3.00}{2.67}\right)=-0.845397=-48.4^{\circ{}}$$

While the book provides +48.4° as the angle.

Am I correct? You can solve (c) from (a) and (b) [my answers are identical to those of the book].

It is from Fundamentals of Physics (Extended) - 9th ed.

 

[Mangoes]

Well, without thinking too much about it, the vector given in (a) is in the fourth quadrant. The angle 48.4° is in the first quadrant. Your answer, however, is definitely in the fourth quadrant.

 

[TSny]

You are correct. The text should not have stated the answer as simply 48.4^o.
If they had stated it as 48.4^o below the positive x direction, then that would have been a good answer. But they didn't.

 

[mafagafo]

Yes, that's what I thought. I was pretty sure I was right, but as this book has presented very few mistakes already I thought I could be missing something.

Thank you guys for looking at it.

 

[HalfLostAndSearching]

by Halliday et al.I would first like to commend you for checking and verifying your answers instead of blindly accepting the textbook's answer. This is an important practice in science and shows critical thinking skills.

Based on your calculations, it seems like your answer for (c) is correct. The angle should be calculated using the inverse tangent function, which gives a negative value in this case. The textbook's answer of +48.4° is incorrect and should be -48.4°.

I would suggest bringing this discrepancy to your teacher's attention so that they can address it in class and make sure all students have the correct information. As scientists, it is important for us to always question and verify information, especially in textbooks which are meant to be reliable sources of information.

In the future, if you come across any other discrepancies or incorrect information in textbooks, it is important to bring it to the attention of your teacher or professor so that they can address it and provide the correct information to all students. This will help ensure that everyone has the correct understanding of the subject matter.