A duck is swimming across a river. The duck can swim at maximum speed of 2m\s in still water. If the duck i swimming as hard as possible straight across a river that running at 4m\s, what is the duck's overall speed, relative to the goose sitting on the river bank?
you're adding two vectors
2^2 + 4^2 = s^2
To find the duck's overall speed relative to the goose, we can use the concept of vector addition. The duck's overall speed will be the magnitude of the resultant vector formed by adding the duck's swimming velocity and the river's velocity.
Let's assume that the river is flowing horizontally from left to right. The duck is swimming perpendicular to the river flow, from one bank to the other.
The duck's swimming velocity is 2 m/s in still water, and we can represent it as a vector with only a horizontal component.
The river's velocity is 4 m/s horizontally from left to right, and we can represent it as a vector with only a horizontal component.
Since the duck is swimming straight across the river, the vertical component of its velocity is zero.
To find the overall speed of the duck, we need to find the magnitude of the resultant vector, which is formed by adding the duck's swimming velocity vector and the river's velocity vector.
Using the Pythagorean theorem, we can calculate the magnitude of the resultant vector:
Resultant velocity^2 = (Duck's velocity)^2 + (River's velocity)^2
Resultant velocity^2 = (2 m/s)^2 + (4 m/s)^2
Resultant velocity^2 = 4 m^2/s^2 + 16 m^2/s^2
Resultant velocity^2 = 20 m^2/s^2
Taking the square root of both sides:
Resultant velocity = √(20 m^2/s^2)
Resultant velocity ≈ 4.47 m/s
Therefore, the duck's overall speed, relative to the goose sitting on the river bank, is approximately 4.47 m/s.
To determine the duck's overall speed relative to the goose, you need to consider the vectors involved in the problem.
The duck's maximum swimming speed in still water is 2m/s. This represents the duck's speed directly across the river (perpendicular to the river's flow).
The river is flowing at a speed of 4m/s. This represents the river's speed relative to the river bank.
To calculate the duck's overall speed, you can apply vector addition. The overall speed is the vector sum of the duck's speed in still water and the river's speed.
Using the Pythagorean theorem, you can find the magnitude of the overall speed:
Overall speed = √(duck's speed^2 + river's speed^2)
Overall speed = √(2^2 + 4^2)
Overall speed = √(4 + 16)
Overall speed = √20
Overall speed ≈ 4.47 m/s
Therefore, the duck's overall speed, relative to the goose sitting on the river bank, is approximately 4.47 m/s.