Problem: A man is crossing a river flowing velocity of 5 m/sec. He reaches a point directly across at a distance of 60 m in 5 sec. His velocity in still water should be?

Solution:

To solve this problem, we need to use the concept of relative velocity. When a person is moving with respect to a stationary object, then the relative velocity of the person is the difference between the velocity of the person and the velocity of the stationary object. In this problem, the stationary object is the riverbank, and the person is moving with respect to the river.

Given parameters:

- Velocity of the river = 5 m/sec
- Distance traveled by the person = 60 m
- Time taken by the person = 5 sec

We can calculate the velocity of the person with respect to the water using the formula:

velocity of the person with respect to the water = Distance / Time

velocity of the person with respect to the water = 60 / 5 = 12 m/sec

Now, let us assume that the velocity of the person in still water is v and the velocity of the river is u. Then, the velocity of the person with respect to the ground can be calculated using the formula:

velocity of the person with respect to the ground = velocity of the person with respect to the water + velocity of the river

velocity of the person with respect to the ground = v + 5

We know that the person reaches a point directly across the river in 5 seconds. Therefore, the distance covered by the person with respect to the ground is 60 meters. We can use this information to form an equation:

60 = (v + 5) x 5

Simplifying the above equation, we get:

v + 5 = 12

v = 7 m/sec

Therefore, the velocity of the person in still water is 7 m/sec.

Conclusion:

The velocity of the person in still water is 7 m/sec.