van can swim 3.0 m/s in still water. while trying to swim directly across a river from west to east, van is pulled by a current flowing southward at 2.0 m/s. what is the magnitude of van's resultant velocity?
sqrt(9+4)
To find the magnitude of Van's resultant velocity, we can use the concept of vector addition. The resultant velocity is the vector sum of the velocity in still water and the velocity due to the current.
Let's break down the problem:
- Van's speed in still water is 3.0 m/s.
- The current is flowing southward at a speed of 2.0 m/s.
Since Van wants to swim directly across the river from west to east, we need to find the horizontal component of the resultant velocity.
The horizontal component of Van's velocity is the same as the velocity in still water, as it is not affected by the current. So, the horizontal component of the resultant velocity is 3.0 m/s.
Now, to find the vertical component of the resultant velocity, we need to take into account the current's influence. The vertical component is the speed of the current, which is 2.0 m/s.
To calculate the magnitude of the resultant velocity, we can use the Pythagorean theorem:
Resultant velocity (magnitude) = √((horizontal velocity)^2 + (vertical velocity)^2)
In this case:
Resultant velocity = √((3.0 m/s)^2 + (2.0 m/s)^2)
= √(9.0 m^2/s^2 + 4.0 m^2/s^2)
= √(13.0 m^2/s^2)
≈ 3.61 m/s
Therefore, the magnitude of Van's resultant velocity is approximately 3.61 m/s.