A person can directly cross a river of width 100 m in 4 minutes when there is no current, but it takes 5 minutes when there is current. What is the velocity of the current?
Nuts to this problem. If one is moving across the river, the v=25m/s.
If a current is at 90 degrees to the direction across the river, the time to get across is still 4 min. Now they may be moving downstream at some rate, but that does not affect how long it takes to get across. So the velocity of the current can be anything, it does not affect time to get across.
To determine the velocity of the current, we need to understand the relationship between time, distance, and velocity.
Let's assume the speed of the person (or the boat) in still water is "x" m/minute, and the velocity of the current is "v" m/minute. When the person is going with the current, the effective speed will be the sum of their speed in still water and the speed of the current. On the other hand, when going against the current, the effective speed will be the difference between their speed in still water and the speed of the current.
In this case, we have the following situations:
1. Without current: The person crosses the river of width 100m in 4 minutes. So, in this case, the distance they travel is 100m and the time is 4 minutes. Therefore, the speed in still water is given by: speed = distance / time = 100m / 4min = 25m/min.
2. With current: The person crosses the same river of width 100m in 5 minutes. So, in this case, the distance they travel is 100m and the time is 5 minutes. Therefore, the speed in still water + the speed of the current is given by: speed = distance / time = 100m / 5min = 20m/min.
Now, we can determine the velocity of the current by subtracting the speed in still water (25m/min) from the speed with the current (20m/min):
velocity of the current = speed with current - speed in still water
= 20m/min - 25m/min
= -5m/min
Hence, the velocity of the current is 5m/min in the opposite direction of the person's motion.