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 700. m, it is heading 35.0° south of east. find the radius of curvature of its path. (use the correct number of significant figures.)

Answer 1

The car had traveled 90 - 35 = 55°

 

Converting to rad:

55° * (2π rad / 360°) = 0.96 rad

length of arc = radius * rad of angle 
700 m = R * 0.96 
R = 729.17 m 

Answer 2

Answer:

The radius of the curvature is 1145.7 meters.

Step-by-step explanation:

We are given that,

Distance measured around the curvature, s = 700 meters

Angle measured, θ = 35° = 0.611 radians

Using $s=r\theta$, we will find the radius of the circle traced by the car.

So, on substituting the values, we get,

$s=r\theta$

implies $700=r\times 0.611$

i.e. $r=\frac{700}{0.611}$

i.e. r = 1145.7 meters.

Hence, the radius of the curvature is 1145.7 meters.