A student runs toward a vertical plane mirror at 5 m/s while the mirror, mounted on wheels, approaches her at 3 m/s. The speed at which her image moves, relative to the ground, is
Choices: 13, 16, 8, 11, 2 m/s
To solve this problem, we need to use the concept of relative velocity.
Let's assume that the student is moving to the right, and the mirror is moving to the left. Therefore, the velocity of the student is positive (+5 m/s), and the velocity of the mirror is negative (-3 m/s).
The relative velocity is the difference between the velocities of the student and the mirror. In this case, it is calculated by adding their velocities since they are moving in opposite directions:
Relative velocity = Velocity of student + Velocity of mirror
Relative velocity = +5 m/s + (-3 m/s)
Relative velocity = 5 m/s - 3 m/s
Relative velocity = +2 m/s
Therefore, the speed at which her image moves, relative to the ground, is 2 m/s.
In conclusion, the correct choice is 2 m/s.
To determine the speed at which the student's image moves relative to the ground, we can break down the motion into two components: the student's motion towards the mirror and the mirror's motion towards the student.
Let's consider the motion of the student. The student is running towards the mirror at a speed of 5 m/s. Since the mirror is stationary relative to the student, the speed of the mirror does not affect the speed of the student towards the mirror. Therefore, the student's speed towards the mirror remains at 5 m/s.
Now let's consider the motion of the mirror. The mirror is moving towards the student at a speed of 3 m/s. Since the image in the mirror is formed by the reflection of light, the image will appear as if it is coming from behind the mirror. Consequently, the image of the student will also appear to be moving towards the mirror at the same speed as the mirror itself. Therefore, the speed of the student's image, relative to the ground, is also 3 m/s.
To find the total speed of the student's image relative to the ground, we can add the speeds of the student and the mirror. So, 3 m/s + 5 m/s = 8 m/s.
Therefore, the speed at which the student's image moves, relative to the ground, is 8 m/s.
Choice: 8 m/s.