SOLUTION: The tangent of the proper banking angle θ of the road for a car making a turn is directly proportional to the square of the car’s velocity v and inversely proportional to the

Question 1197651: The tangent of the proper banking angle θ of the road for a car
making a turn is directly proportional to the square of the car’s
velocity v and inversely proportional to the radius r of the turn.
7.75° is the proper banking angle for a car travelling at 20.0 m/s
around a turn of radius 300m.What is the proper banking angle
for a car travelling at 30.0 m/s around a turn of radius 250 m?
Thank you
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
The tangent of the proper banking angle θ of the road for a car
making a turn is directly proportional to the square of the car’s
velocity v and inversely proportional to the radius r of the turn.
7.75° is the proper banking angle for a car travelling at 20.0 m/s
around a turn of radius 300m.What is the proper banking angle
for a car travelling at 30.0 m/s around a turn of radius 250 m?


Write the "k-equation":

 =  




Substitute the information from the situation when ALL the quantities 
are given (except k):



Solve for k:

Multiply both sides by 300





Make sure your calculator is in degree mode and not radian mode:





Divide both sides by 400



Substitute the value of k in the first equation:



Substitute the information from the other situation when all 
the variables BUT ONE are given:



Calculate the right side:



Solve for the missing variable, which in this case is "θ":

Use the inverse tangent function on your calculator



Since the given angle was rounded to hundredths, round your final
answer the same way:



Edwin

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