The radius of the curved road at the given condition is 54.1 m.
The given parameters:
- <em>mass of the car, m = 1000 kg</em>
- <em>speed of the car, v = 50 km/h = 13.89 m/s</em>
- <em>banking angle, θ = 20⁰</em>
The normal force on the car due to banking curve is calculated as follows;
![Fcos(\theta) = mg](https://tex.z-dn.net/?f=Fcos%28%5Ctheta%29%20%3D%20mg)
The horizontal force on the car due to the banking curve is calculated as follows;
![Fsin(\theta) = \frac{mv^2}{r}](https://tex.z-dn.net/?f=Fsin%28%5Ctheta%29%20%3D%20%5Cfrac%7Bmv%5E2%7D%7Br%7D)
<em>Divide </em><em>the second equation by the first;</em>
![\frac{Fsin(\theta)}{Fcos(\theta) } = \frac{mv^2}{rmg} \\\\tan(\theta) = \frac{v^2}{rg} \\\\r = \frac{v^2}{g \times tan(\theta)} \\\\r = \frac{13.89^2}{9.8 \times tan(20)} \\\\r = 54.1 \ m](https://tex.z-dn.net/?f=%5Cfrac%7BFsin%28%5Ctheta%29%7D%7BFcos%28%5Ctheta%29%20%7D%20%3D%20%5Cfrac%7Bmv%5E2%7D%7Brmg%7D%20%5C%5C%5C%5Ctan%28%5Ctheta%29%20%3D%20%5Cfrac%7Bv%5E2%7D%7Brg%7D%20%5C%5C%5C%5Cr%20%3D%20%5Cfrac%7Bv%5E2%7D%7Bg%20%5Ctimes%20tan%28%5Ctheta%29%7D%20%5C%5C%5C%5Cr%20%3D%20%5Cfrac%7B13.89%5E2%7D%7B9.8%20%5Ctimes%20tan%2820%29%7D%20%5C%5C%5C%5Cr%20%3D%2054.1%20%5C%20m)
Thus, the radius of the curved road at the given condition is 54.1 m.
Learn more about banking angle here: brainly.com/question/8169892
When there's a hazard ahead, it's almost always quicker for you to steer away than to come to a full stop.
<h3>What is an hazard?</h3>
Hazard refers to any obstacle or other feature which causes risk or danger.
Living organisms respond to hazards via the production of adrenaline hormone. This hormone causes a flight response away from the hazard.
Therefore, when there's a hazard ahead, it's almost always quicker for you to steer away than to come to a full stop.
Learn more about hazards at: brainly.com/question/5338299
Answer: Dark matter.
Explanation: Hope it helps :)