A city planner is working on the redesign of a hilly

Chapter 4, Problem 71

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QUESTION:

A city planner is working on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 920 kg, can accelerate on a level road from rest to in 12.5 s. Using these data, calculate the maximum steepness of a hill.

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QUESTION:

A city planner is working on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 920 kg, can accelerate on a level road from rest to in 12.5 s. Using these data, calculate the maximum steepness of a hill.

ANSWER:

Problem 71

A city planner is working on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 920 kg, can accelerate on a level road from rest to 21 m/s (75 km/h) in  12.5 s. Using these data, calculate the maximum steepness of a hill.

                                                               Step by Step Solution

Step 1 of 3

Free body diagram of car:

 Free body equation for car:

Here,  is the acceleration due to gravity,  is the acceleration of the car, and is the steepness of a hill.

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