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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.

Verified Answer :

metchelle

First, it is important to find the force pushing the car up a hill:

Force = mass * acceleration
F = ma

Where:

a = change of velocity / change of time

F = mΔv / Δt 
F = (920)(21 - 0)/(12.5 - 0)
F = 1545.6 N

Equating this value to the car's y-component:

mg sin (x) = 1545.6

Where:

x = angle of inclination
g = gravity = 9.8 m/s^2
m = mass = 920 kg

(920)(9.8)sin(x) = 1545.6
x = 9.87 degrees.

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