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

Step-by-step explanation:

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

F =
`m * a`

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

F =
`m * a`

=
`1090 * ((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) = (1430.625 N)/((1090 * 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.