Is the Book's Answer to the Relative Velocity Problem Incorrect?

[manjuvenamma]

I raised this question in the courseware section and I got only one response. To improve the response, I am repeating the question here. Please see it.

I got one answer and the book at the receprocal of my answer. This is not just for this problem for several problems of this nature the answer given in the book is similarly reciprocal of mine. I want to just reconfirm who is consistently making this mistake.


1. Homework Statement
Rain is falling down vertically. To a man walking on the road, velocity of rain appears to be 1.5 times his velocity. Then to protect himself from rain, he holds his umbrella at an angle (theta) to the vertical such that tan (theta) =


2. Homework Equations

The relative velocity of rain to man is R-M where R is rain velocity and M is man's velocity.


3. The Attempt at a Solution

Assume the rain velocity vector is R. We can think it is -rJ. J is a unit vector along y axis. r is the magnitude of rain velocity. The negative sign comes because of the direction of rain - down.

Similarly M = mI where I is unit vector along x axis. The relative velocity of rain to man is R-M = -rJ-mI.

The magnitude of R-M is 1.5m (given).

1.5m = sqrt(r^2+m^2) implies m/r = 2/sqrt(5) = tan(theta).

But the answer stated in the book is the reciprocal i.e. sqrt(5)/2. Who is right?

 

[Doc Al]

Do not post the same topic twice.

 

[astrokreng]

it is important to approach this question with a critical and analytical mindset. First, let's clarify the problem and equations involved. The given problem states that a man walking on a road is experiencing rain falling down vertically. The velocity of the rain appears to be 1.5 times his own velocity. The attempt at a solution shows the use of vectors and unit vectors to represent the rain and man's velocity. The relative velocity of rain to man is then calculated as R-M = -rJ-mI, where r and m are the magnitudes of rain and man's velocity, respectively.

The question at hand is whether the answer given in the book is correct or not. It is important to note that the answer stated in the book is the reciprocal of the answer calculated by the person asking the question. This suggests that there may be a mistake in the calculations or equations used.

To determine who is right, we can start by checking the units of the calculated answer. The given problem does not specify any units, but it is safe to assume that the velocities are in meters per second (m/s). The units of the calculated answer (m/r) are m/s, which is correct. However, the units of the answer stated in the book (r/m) are not consistent with the given problem. This could be an indication that the answer in the book is incorrect.

Furthermore, we can also check the logic and reasoning behind the calculations. The attempt at a solution correctly uses the given information and equations to calculate the relative velocity of rain to man. However, the answer stated in the book does not seem to follow the same logic. It is important to note that in this type of problem, the relative velocity is always calculated as the magnitude of the two velocities (rain and man) combined, not their ratio. Therefore, the answer stated in the book may not be logically correct.

In conclusion, based on the units and logic used in the calculations, it can be concluded that the answer given in the book is incorrect. it is important to always critically analyze and question the solutions and answers provided, and to use logic and reasoning to determine the correctness of the answer. It is also beneficial to seek additional responses and opinions to further improve understanding and knowledge.