Question

An athlete runs along a circular track of diameter 80m. The distance travelled and the magnitude of displacement of the athlete when he covers \(\frac{3^{th}}{4}\) of the circle is ( in m)

• A. \(60\pi,40\sqrt2\)
• B. \(40\pi,60\sqrt2\)
• C. \(120\pi,80\sqrt2\)
• D. \(80\pi,120\sqrt2\)

Answer 1

The Correct Option is A

1. Calculate the Radius and Circumference: 

• Diameter \(d = 80\) m
• Radius \(r = \frac{d}{2} = \frac{80}{2} = 40\) m
• Circumference \(C = 2\pi r = 2 \pi (40) = 80\pi\) m

2. Calculate the Distance Traveled:

• Distance traveled \( = \frac{3}{4} \times C = \frac{3}{4} \times 80\pi = 60\pi\) m

3. Calculate the Displacement:

• The athlete is at the end of two perpendicular radii after completing \(\frac{3}{4}\) of the circle.
• Displacement \( = \sqrt{r^2 + r^2} = \sqrt{2r^2} = r\sqrt{2} = 40\sqrt{2}\) m

4. Final Answer:

• Distance traveled: \(60\pi\) m
• Displacement: \(40\sqrt{2}\) m

Therefore, the answer is \(60\pi, 40\sqrt{2}\).