If our circle has 4 m radius and had covered the distance of 14 m on the circumference of a circle. Find the displacement.
Answer: 7.86 m
Explanation
Given:
-
Radius of the circler=4 meters
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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):
θ=s/r=14/4=3.5radians
Step 2: Use the chord length formula to find displacement:
Displacement=2rsin(θ/2)
=2×4×sin(3.5/2)=8×sin(1.75)
sin(1.75radians)≈0.983
Displacement≈8×0.983≈7.864meters
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