A 2.2 m tall object is placed 10.5 m from a truck mirror. If an image is formed -9.75 m from the mirror, what is the height of the image?

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Chapter1: Units, Trigonometry. And Vectors
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**Problem Statement:**

A 2.2 m tall object is placed 10.5 m from a truck mirror. If an image is formed 9.75 m from the mirror, what is the height of the image?

**Solution:**

When dealing with mirrors and the formation of images, we often use the mirror formula and magnification formula. However, for simplicity and clarity, let's walk through this particular problem step by step.

Given:
- Height of the object (h_o) = 2.2 m
- Distance of the object from the mirror (d_o) = 10.5 m
- Distance of the image from the mirror (d_i) = 9.75 m

We assume that the mirror in question is a simple plane mirror or a spherical mirror with small angles involved, allowing for direct proportionality relationships.

**Mirror Magnification Formula:**
\[ \text{Magnification} (m) = \frac{h_i}{h_o} = -\frac{d_i}{d_o} \]

Where:
- \( h_i \) = height of the image
- \( h_o \) = height of the object
- \( d_i \) = distance of the image from the mirror
- \( d_o \) = distance of the object from the mirror

Rearranging this formula to find the height of the image \( h_i \):
\[ h_i = h_o \times \left( -\frac{d_i}{d_o} \right) \]

Substitute the given values:
\[ h_i = 2.2 \times \left( -\frac{9.75}{10.5} \right) \]
\[ h_i = 2.2 \times (-0.9286) \]
\[ h_i \approx -2.04 \text{ m} \]

**Interpretation:**
The negative sign indicates that the image is inverted relative to the object. Therefore, the height of the image is \(2.04 \text{ m}\) (inverted).

**Conclusion:**

The height of the image is 2.04 meters, and it is inverted.

(Note: Ensure to check the context or type of mirror in practical applications, as this problem assumes simple proportionality.)
Transcribed Image Text:**Problem Statement:** A 2.2 m tall object is placed 10.5 m from a truck mirror. If an image is formed 9.75 m from the mirror, what is the height of the image? **Solution:** When dealing with mirrors and the formation of images, we often use the mirror formula and magnification formula. However, for simplicity and clarity, let's walk through this particular problem step by step. Given: - Height of the object (h_o) = 2.2 m - Distance of the object from the mirror (d_o) = 10.5 m - Distance of the image from the mirror (d_i) = 9.75 m We assume that the mirror in question is a simple plane mirror or a spherical mirror with small angles involved, allowing for direct proportionality relationships. **Mirror Magnification Formula:** \[ \text{Magnification} (m) = \frac{h_i}{h_o} = -\frac{d_i}{d_o} \] Where: - \( h_i \) = height of the image - \( h_o \) = height of the object - \( d_i \) = distance of the image from the mirror - \( d_o \) = distance of the object from the mirror Rearranging this formula to find the height of the image \( h_i \): \[ h_i = h_o \times \left( -\frac{d_i}{d_o} \right) \] Substitute the given values: \[ h_i = 2.2 \times \left( -\frac{9.75}{10.5} \right) \] \[ h_i = 2.2 \times (-0.9286) \] \[ h_i \approx -2.04 \text{ m} \] **Interpretation:** The negative sign indicates that the image is inverted relative to the object. Therefore, the height of the image is \(2.04 \text{ m}\) (inverted). **Conclusion:** The height of the image is 2.04 meters, and it is inverted. (Note: Ensure to check the context or type of mirror in practical applications, as this problem assumes simple proportionality.)
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