Velocity of image in plane mirror

[subhradeep mahata]

Homework Statement

A mirror is moving to the right with a velocity 15 m/s, and an object is moving to the right with a speed of 5m/s. All speeds are wrt ground. Find the velocity of image wrt ground.

Homework Equations

The Attempt at a Solution

I present to you two probable solutions:
1) Using formula: V_IMAGE=2V_MIRROR-V_OBJECT
Now, its a mere substitution problem. Using right as positive direction, we get the required velocity as 25m/s to the right.
2) This is a controversial one. I thought about this as i like to explore all the different correct of incorrect methods of a problem.
the above problem is equivalent to: the mirror is moving to the right with a velocity of 10m/s and the object is at rest. Now, substituting in the formula used in the previous method, V_IMAGE=20m/s to the right.

Now, my book says that that the correct answer is 10m/s, but its not matching with any of my answers. Please check it and let me know why both are incorrect.

 

[CWatters]

You could try making two scale drawings, one showing the starting position of the object, mirror and image, and another showing their positions after say 1 second. Figure out how far the image moved in that time.

 

[subhradeep mahata]

Can you please tell me the correct answer?
Yeah, i'll try by that method.

 

[CWatters]

PS: Book answers are sometimes wrong.

 

[CWatters]

Can you please tell me the correct answer?
Yeah, i'll try by that method.

Forum rules discourage us from giving the answer.

 

[gneill]

Sometimes changing your frame of reference can be helpful to clarify what is happening. Suppose you were an observer riding along with the mirror. What is the motion of the object from that point of view? Is it approaching or receding from you? How quickly?