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?
<pre>

Write the "k-equation":

{{{First_quantity_mentioned}}} = {{{k*expr((product_of_all_directlys_ or_jointlys_or_1_if_none)/(product_of_all_inverselys_or_1_if_none))}}} 

{{{tan(theta)}}}{{{""=""}}}{{{k*expr(v^2/r^"")}}}


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

{{{tan(7.75^o)}}}{{{""=""}}}{{{k*expr(20.0^2/300^"")}}}

Solve for k:

Multiply both sides by 300

{{{300tan(7.75^o)}}}{{{""=""}}}{{{k*20.0^2}}}

{{{300tan(7.75^o)}}}{{{""=""}}}{{{k*20.0^2}}}

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

{{{300(0.1360940271)}}}{{{""=""}}}{{{k*400}}}

{{{40.82820812)}}}{{{""=""}}}{{{k*400}}}

Divide both sides by 400

{{{0.1020705203)}}}{{{""=""}}}{{{k}}}

Substitute the value of k in the first equation:

{{{tan(theta)}}}{{{""=""}}}{{{0.1020705203*expr(v^2/r^"")}}}

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

{{{tan(theta)}}}{{{""=""}}}{{{0.1020705203*expr(30.0^2/250^"")}}}

Calculate the right side:

{{{tan(theta)}}}{{{""=""}}}{{{0.3674538731}}}

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

Use the inverse tangent function on your calculator

{{{theta}}}{{{""=""}}}{{{20.17605163^o}}}

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

{{{theta}}}{{{""=""}}}{{{20.18^o}}}

Edwin</pre>