If our circle has 4 m radius and had covered the distance of 14 m on the circumference of a circle. Find the displacement.

4.00 m

6.20 m

7.86 m

8.00 m

Explanation

Given:

Radius of the circle $r = 4$ meters
Arc length (distance along the circumference), $s = 14$ meters

We are to find the displacement, which is the straight-line distance between the starting and ending points of the arc.

Step 1: Find the angle subtended by the arc at the center (θ in radians):

$theta = frac{s}{r} = frac{14}{4} = 3.5 , text{radians}$

Step 2: Use the chord length formula to find displacement:

$Displacement = 2 r sin (θ/2)$ $= 2 \times 4 \times sin (3.5/2) = 8 \times sin (1.75)$ $sin (1.75 radians) \approx 0.983$ $Displacement \approx 8 \times 0.983 \approx 7.864 meters$