# A car is running in a circular path with 22 kmph speed the radius is 14 km.find the distance and displacement travelled in 5 hours? we know that the distance covered is 110 km how to calculate displacement

2
by pavankumar

2015-05-17T22:35:40+05:30
I think this diagram will help u
from calculation length of the arc ab(S) = (110-2πR) (R is the radius of the circle)
you can use the formula S = R(2θ) to get θ ( θ is in radian)
so length of the chord becomes 2(Rsinθ)
which is ur ans
i have given u the procedure

2015-05-18T03:36:58+05:30

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Distance covered = speed * time duration = 22 kmph * 5 hrs
s = 110 km

Let the center of the  circle be  O.  Let the point of departure be A.  Let the point where the car is after 5 hours  be  B.

=>  Ф = 110 km / 14 km
= 55/7 radians = 22/7 * 5/2 = 5/2 * π  radians
Ф = 2 π + π/2 radians

=> the car has completed one full circle and then reached a point B such that the angle BOA  is  90 deg.

So,  BOA is a right angle triangle.  The displacement is the diagonal of the triangle.  OB and OA are radii.  Hence AB = displacement = √2 * radius

displacement = √2 * 14 km
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you can also find the displacement by:

distance covered = 110 km
perimeter of the circle = 2 π * 14 km = 2 * 22/ 7 * 14 = 88 km

distance / perimeter = 110 / 88 = 10/8 = 5/4  = 1 + 1/4

This means that the car has completed one complete revolution and did one quarter.  So  the triangle  OAB will be a right angle triangle, with  OA and OB as radii and AB as the displacement.

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