In designing a freeway on-ramp, you must make it long enough for cars to be able to accelerate and merge safely with traffic traveling at speeds of 70 mph. For an off-ramp, the cars must be able to come to a stop from 35 mph over the length of the ramp. Your traffic engineers provide the following data: Powerful cars can accelerate from rest to 50 mph in 5.2 s, while less powerful cars take twice as long to do this. When slowing down from 35 mph, a car with good tire treads will take 8.4 s to stop, whereas one with bald tires takes 16.6 S. Part A In order to safely accommodate all the types of vehicles, what should be the minimum length (in meters) of on-ramps? Express your answer using two significant figures. Lon= Part B V ΑΣΦ Loff = ? In order to safely accommodate all the types of vehicles, what should be the minimum length (in meters) of off-ramps? Express your answer using two significant figures. VO ΑΣΦ m ? m

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**Designing Freeway Ramps: A Practical Guide**

When designing a freeway on-ramp, it is crucial to ensure cars can accelerate and merge safely with traffic traveling at speeds of 70 mph. Similarly, for off-ramps, cars must be capable of coming to a complete stop from 35 mph over the length of the ramp. Traffic engineers have provided the following data to assist in this task:

- **Powerful Cars:** Can accelerate from rest to 50 mph in 5.2 seconds.
- **Less Powerful Cars:** Require twice as much time to reach the same speed.
- **Stopping Distances:**
  - With good tire treads, a car will take 8.4 seconds to stop from 35 mph.
  - With bald tires, the stopping time increases to 16.6 seconds.

**Part A: On-Ramp Design**

To accommodate all vehicles safely, the following question is posed:

"What should be the minimum length (in meters) of on-ramps?"

Please express your answer using two significant figures.

\( L_{on} = \) ______ m

**Part B: Off-Ramp Design**

To ensure safety for all vehicles, determine:

"What should be the minimum length (in meters) of off-ramps?"

Provide your answer with two significant figures.

\( L_{off} = \) ______ m

This guide is an essential resource for ensuring the safe and efficient design of freeway entrance and exit ramps.
Transcribed Image Text:**Designing Freeway Ramps: A Practical Guide** When designing a freeway on-ramp, it is crucial to ensure cars can accelerate and merge safely with traffic traveling at speeds of 70 mph. Similarly, for off-ramps, cars must be capable of coming to a complete stop from 35 mph over the length of the ramp. Traffic engineers have provided the following data to assist in this task: - **Powerful Cars:** Can accelerate from rest to 50 mph in 5.2 seconds. - **Less Powerful Cars:** Require twice as much time to reach the same speed. - **Stopping Distances:** - With good tire treads, a car will take 8.4 seconds to stop from 35 mph. - With bald tires, the stopping time increases to 16.6 seconds. **Part A: On-Ramp Design** To accommodate all vehicles safely, the following question is posed: "What should be the minimum length (in meters) of on-ramps?" Please express your answer using two significant figures. \( L_{on} = \) ______ m **Part B: Off-Ramp Design** To ensure safety for all vehicles, determine: "What should be the minimum length (in meters) of off-ramps?" Provide your answer with two significant figures. \( L_{off} = \) ______ m This guide is an essential resource for ensuring the safe and efficient design of freeway entrance and exit ramps.
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