**Problem Statement:**A ranger in a national park is driving at 22.0 mi/h when a deer jumps into the road 180 ft ahead of the vehicle. After a reaction time \( t \), the ranger applies the brakes to produce an acceleration of \( a = -8.00 \, \text{ft/s}^2 \). What is the maximum reaction time allowed if she is to avoid hitting the deer?**Concepts Involved:**- **Uniform Motion and Deceleration:** Understanding how initial velocity, acceleration, and distance relate in uniformly accelerated linear motion.- **Kinematic Equations:** Using equations to determine time, distance, and velocity.This problem involves converting the vehicle's speed from miles per hour to feet per second, calculating the stopping distance using kinematic equations, and then determining the reaction time.---1. **Speed Conversion:** - \( \text{Velocity in ft/s} = 22.0 \, \text{mi/h} \times \frac{5280 \, \text{ft/mi}}{3600 \, \text{s/h}} \) 2. **Maximum Stopping Distance Equation:** - Use \( v^2 = u^2 + 2as \) where \( v = 0 \) (final velocity), \( u \) is initial velocity, \( a \) is acceleration, and \( s \) is stopping distance.3. **Calculate Reaction Time:** - Find the total distance the vehicle travels during the driver's reaction time and braking to ensure it does not exceed 180 ft.---Teaching Notes:- Analyzing reaction time and braking distance in real-life situations can help understand safety measures and the physics of motion.- Encourage students to think about variables that may affect the outcome, such as road conditions and vehicle maintenance.

Name: **Problem Statement:**A ranger in a national park is driving at 22.0
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Description: **Problem Statement:**A ranger in a national park is driving at 22.0 mi/h when a deer jumps into the road 180 ft ahead of the vehicle. After a reaction time \( t \), the ranger applies the brakes to produce an acceleration of \( a = -8.00 \, \text{f

The initial velocity of a ranger is, u=22 mi/hr=9.835 m/s The final velocity of a ranger is, v=0 m/s…

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A ranger in a national park is driving at 22.0 mi/h when a deer jumps into the road 180 ft ahead of the vehicle. After a reaction time t, the ranger applies the brakes to produce an acceleration of a = -8.00 ft/s2. What is the maximum reaction time allowed if she is to avoid hitting the deer? %3D

A ranger in a national park is driving at 22.0 mi/h when a deer jumps into the road 180 ft ahead of the vehicle. After a reaction time t, the ranger applies the brakes to produce an acceleration of a = -8.00 ft/s2. What is the maximum reaction time allowed if she is to avoid hitting the deer? %3D

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Displacement, Velocity and Acceleration

In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.

Linear Displacement

The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.

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Question

**Problem Statement:**

A ranger in a national park is driving at 22.0 mi/h when a deer jumps into the road 180 ft ahead of the vehicle. After a reaction time \( t \), the ranger applies the brakes to produce an acceleration of \( a = -8.00 \, \text{ft/s}^2 \). What is the maximum reaction time allowed if she is to avoid hitting the deer?

**Concepts Involved:**

- **Uniform Motion and Deceleration:** Understanding how initial velocity, acceleration, and distance relate in uniformly accelerated linear motion.
- **Kinematic Equations:** Using equations to determine time, distance, and velocity.

This problem involves converting the vehicle's speed from miles per hour to feet per second, calculating the stopping distance using kinematic equations, and then determining the reaction time.

---

1. **Speed Conversion:**
- \( \text{Velocity in ft/s} = 22.0 \, \text{mi/h} \times \frac{5280 \, \text{ft/mi}}{3600 \, \text{s/h}} \)

2. **Maximum Stopping Distance Equation:**
- Use \( v^2 = u^2 + 2as \) where \( v = 0 \) (final velocity), \( u \) is initial velocity, \( a \) is acceleration, and \( s \) is stopping distance.

3. **Calculate Reaction Time:**
- Find the total distance the vehicle travels during the driver's reaction time and braking to ensure it does not exceed 180 ft.

---

Teaching Notes:
- Analyzing reaction time and braking distance in real-life situations can help understand safety measures and the physics of motion.
- Encourage students to think about variables that may affect the outcome, such as road conditions and vehicle maintenance.

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