Another Physics Question...?

Question

A highway curve forms a section of a circle. A car goes around the curve. Its dashboard compass shows that the car is initially heading due east. After it travels 855 m, it is heading 37.0° south of east. Find the radius of curvature of its path. Suggestion: Use s = r θ where θ is in radians.

Can you show me the steps as to how you got to that answer? Thanx!! :-)

Answer 1

37.0°=π/180rad

curve / radius =radians

radius = curve /radians

           =855/[π/180]

           =(855 x 180) / π

           =153900 / π

           =48987.8914836853843496624223660

Answer 2

First step in a problem is to list knowns and unkowns:

Dist around curvature measured = 855 m

Angle of curvature measured = 37 degrees

Unkown is the radius of the circle being traced by the car

Using the provided formula s = r times theta.  This describes the circumference (s) that is traced out on a circle in moving theta angle.  You know s and you know theta

s= r * theta

855m = r * 37 degrees * 2 Pi radians/360 degrees (I just converted degrees to radians to make the formula valid)

855m/37degrees /2/Pi radians*360 degrees= r

r = 1324 meters keeping the units the same