During a practice session in a stadium an athlete runs along a circular track and her performance is observed by her coach standing at a point on the circle and also by her physiotherapist standing at the centre of the circle. The coach finds that she covers an angle of `72^(@)` in 1 min. What will be the angle covered by her in 1 second according to the measurement made by her physiotherapist?

Options

A. A) It depends on the position of the coach on the circular track
B. B) `1.2^(@)`
C. C) `4.8^(@)`
D. D) `2.4^(@)`

Answer

To solve the problem step by step, we need to find out how much angle the athlete covers in one second according to the physiotherapist standing at the center of the circular track.

### Step 1: Understand the given information
The coach observes that the athlete covers an angle of 72 degrees in 1 minute.

**Hint:** Identify the key information provided in the problem, which includes the angle covered and the time duration.

### Step 2: Determine the angle covered in one minute
The angle covered by the athlete in one minute is given as 72 degrees.

**Hint:** Remember that the time duration is crucial for calculating the angle per second.

### Step 3: Use the relationship between angles at the center and circumference
According to the properties of circles, the angle subtended at the center of the circle (by the same arc) is twice the angle subtended at any point on the circumference. Therefore, the angle at the center (measured by the physiotherapist) will be:
\[ \text{Angle at center} = 2 \times \text{Angle at circumference} \]
\[ \text{Angle at center} = 2 \times 72^\circ = 144^\circ \]

**Hint:** Recall the geometric property that relates angles at the center and the circumference of a circle.

### Step 4: Calculate the angle covered in one minute according to the physiotherapist
The angle covered by the athlete in one minute, as observed by the physiotherapist, is 144 degrees.

**Hint:** Make sure to keep track of which observer is measuring the angle.

### Step 5: Find the angle covered in one second
To find the angle covered in one second, we need to divide the angle covered in one minute by the number of seconds in a minute:
\[ \text{Angle per second} = \frac{144^\circ}{60} \]

Calculating this gives:
\[ \text{Angle per second} = 2.4^\circ \]

**Hint:** Remember that there are 60 seconds in a minute when converting from minutes to seconds.

### Step 6: Conclusion
Thus, the angle covered by the athlete in one second according to the measurement made by her physiotherapist is **2.4 degrees**.

**Final Answer:** 2.4 degrees