You unconsciously estimate the distance to an object from the angle it subtends in your field of view. This angle 8 in radians is related to the linear height of the object h and to the distance d by 0 h/d. Assume that you are driving a car and that another car, 1.50 m high, is 22.0 m behind you. O d) What anal OBJECTS IN MARCR ARE. CLOSER THAN THEY APPEAR REG O (a) Suppose your car has a flat passenger-side rearview mirror, 1.55 m from your eyes. How far from your eyes is the image of the car following you? m (b) What angle does the image subtend your field of view? rad (c) Suppose instead your car has a convex rearview mirror (see figures) with a radius of curvature of magnitude 1.70 m. How far from your eyes is the image of the car following you? m

College Physics
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Chapter1: Units, Trigonometry. And Vectors
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**Educational Text Transcription:**

You unconsciously estimate the distance to an object from the angle it subtends in your field of view. This angle θ in radians is related to the linear height of the object \( h \) and to the distance \( d \) by \( θ = h/d \). Assume that you are driving a car and that another car, 1.50 m high, is 22.0 m behind you.

**Image Descriptions:**

1. **Photo Description:**
   - A photo of a passenger-side rearview mirror displaying the typical warning: "Objects in mirror are closer than they appear." In the reflection, a large truck is seen behind the car.

2. **Cartoon Illustration:**
   - A cartoon depicts a woman looking into the rearview mirror while driving, with the mirror showing a close-up of a car behind and the same warning text.

**Questions:**

(a) Suppose your car has a flat passenger-side rearview mirror, 1.55 m from your eyes. How far from your eyes is the image of the car following you?
- **Answer:**
  \[\_\_\_\_\] m

(b) What angle does the image subtend in your field of view?
- **Answer:**
  \[\_\_\_\_\] rad

(c) Suppose instead your car has a convex rearview mirror (see figures) with a radius of curvature of magnitude 1.70 m. How far from your eyes is the image of the car following you?
- **Answer:**
  \[\_\_\_\_\] m

(d) What angle does the image subtend at your eyes?
- **Answer:**
  \[\_\_\_\_\] rad

(e) Based on its angular size, how far away does the following car appear to be?
- **Answer:**
  \[\_\_\_\_\] m
Transcribed Image Text:**Educational Text Transcription:** You unconsciously estimate the distance to an object from the angle it subtends in your field of view. This angle θ in radians is related to the linear height of the object \( h \) and to the distance \( d \) by \( θ = h/d \). Assume that you are driving a car and that another car, 1.50 m high, is 22.0 m behind you. **Image Descriptions:** 1. **Photo Description:** - A photo of a passenger-side rearview mirror displaying the typical warning: "Objects in mirror are closer than they appear." In the reflection, a large truck is seen behind the car. 2. **Cartoon Illustration:** - A cartoon depicts a woman looking into the rearview mirror while driving, with the mirror showing a close-up of a car behind and the same warning text. **Questions:** (a) Suppose your car has a flat passenger-side rearview mirror, 1.55 m from your eyes. How far from your eyes is the image of the car following you? - **Answer:** \[\_\_\_\_\] m (b) What angle does the image subtend in your field of view? - **Answer:** \[\_\_\_\_\] rad (c) Suppose instead your car has a convex rearview mirror (see figures) with a radius of curvature of magnitude 1.70 m. How far from your eyes is the image of the car following you? - **Answer:** \[\_\_\_\_\] m (d) What angle does the image subtend at your eyes? - **Answer:** \[\_\_\_\_\] rad (e) Based on its angular size, how far away does the following car appear to be? - **Answer:** \[\_\_\_\_\] m
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