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. 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.

Answer 1

Explanation:

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

                      F = $m \times a$

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

              F = $m \times a$      

                 = $1090 \times (\frac{21}{16})$

                 = 1430.625 N

Also, it is known that

      $sin(\theta) = \frac{\text{Force car can exert}}{\text{Force gravity pulls car}}$

      $sin(\theta) = \frac{1430.625 N}{(1090 \times 9.8) N}$

        $\theta$ = 7.70 degrees

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