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. It is given that a particular small car, with a mass of 1090 kg, can accelerate on a level road from rest to 21 m/s (75.6 km/h) in 16.0 s. Using this data, calculate the maximum steepness of a hill.

Explanation:

It is known that relation between force and acceleration is as follows.

                      F =

I is given that, mass is 1090 kg and acceleration is 21 m/s. Therefore, we will calculate force as follows.

              F =      

                 =

                 = 1430.625 N

Also, it is known that

        = 7.70 degrees

Thus, we can conclude that the maximum steepness for the car to still be able to accelerate is 7.70 degrees.

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