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
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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
now your task is to do the necessary calculation
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
now your task is to do the necessary calculation
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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.
arc length = radius * angle Ф in radians
=> 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.
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.
arc length = radius * angle Ф in radians
=> 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
==============================
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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