Chapter 13.2, Problem 35PPS

To determine

Calculate the time taken for the minute hand on a clock to pass $2.5\pi$ radians.

Answer to Problem 35PPS

The time taken to pass $2.5\pi$ radian is $75\min utes$ .

Explanation of Solution

Given: It is given in the question that the angle is $2.5\pi$ radian.

Concept Used:

In this, use the concept of knowing the fact that full circle has $2\pi$ radians and a quarter circle has $0.5\pi$ radian.

Calculation: Since, it is known that the full circle has $2\pi$ radians.

Now, it is easy to conclude that $0.5\pi$ radian is equal to quarter of the circle.

Now, it is known that the minute hand on a clock pass one whole circle ( $60$ minutes) and a quarter of the circle ( $15$ minutes)

So, add this two number to find out that the minute hand on a clock needs $75$ minutes $(60+15\min utes)$ to pass $2.5\pi$ radians.

Conclusion:

The time taken is $75\min utes$ .