Answer:
We can solve this problem by using the concept of relative motion. Let's assume that the first boy is running in the clockwise direction and the second boy is chasing him in the counterclockwise direction.
Since the second boy always remains on the radius connecting the center of the circle and the first boy, the distance between them is always equal to the radius of the circle, which is 28 m.
Let's denote the distance covered by the first boy as S1 and the distance covered by the second boy as S2. We know that the first boy is running with a constant speed of 4 m/s, so we can write:
S1 = u*t1
where t1 is the time taken by the first boy to complete the chase.
The second boy is moving with a constant velocity of 4 m/s towards the first boy, so we can write:
S2 = V*t2
where t2 is the time taken by the second boy to catch up with the first boy.
Since the second boy is always moving on the radius connecting the center of the circle and the first boy, the distance covered by him is equal to the distance on the circumference of the circle covered by the first boy, minus the distance covered by the first boy along the radius. We can write:
S2 = S1 - 2*pi*R
where pi is the mathematical constant pi (approximately equal to 3.14).
Substituting the values of S1 and S2, we get:
u*t1 = V*t2 + 2*pi*R
Since the time of chase is (10 + x) sec, we can also write:
t1 + t2 = 10 + x
We have two equations and two unknowns (t1 and t2), so we can solve for them. First, we can solve for t2:
t2 = (u*t1 - 2*pi*R) / V
Substituting this in the second equation, we get:
t1 + (u*t1 - 2*pi*R) / V = 10 + x
Simplifying this equation, we get:
t1*(1 + u/V) = 10 + x + 2*pi*R/V
Finally, we can solve for t1:
t1 = (10 + x + 2*pi*R/V) / (1 + u/V)
Substituting the given values of R, u, and V, we get:
t1 = (10 + x + 56*pi) / 20
Simplifying this expression, we get:
t1 = 2.8*pi + 0.5*x + 2.8
Therefore, the time taken by the first boy to complete the chase is 2.8*pi + 0.5*x + 2.8 seconds.
Step-by-step explanation:
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