A man who can row in still water at 3 mph heads directly across a river flowing at 7 mph.
At what speed does he drift downstream?
To find the speed at which the man drifts downstream, we can use the concept of vector addition.
First, let's define the velocities involved:
- The man's velocity in still water is 3 mph (miles per hour).
- The river's velocity is 7 mph, flowing directly across.
To determine the man's drift downstream, we need to find the resultant velocity, which is the vector sum of the man's velocity in still water and the river's velocity.
To calculate the resultant velocity, we can use the Pythagorean theorem:
Resultant Velocity^2 = (Man's Velocity)^2 + (River's Velocity)^2
Let's substitute the values:
Resultant Velocity^2 = 3^2 + 7^2
Resultant Velocity^2 = 9 + 49
Resultant Velocity^2 = 58
Taking the square root of both sides to solve for the resultant velocity:
Resultant Velocity = √58
Therefore, the man drifts downstream at approximately 7.62 mph (rounded to two decimal places), when the river's velocity is 7 mph and the man's velocity in still water is 3 mph.
x^2 = 3^2 + 7^2
x = ....