What is the resultant of a vector that has components 25 m/s east, and 25 m/s north?

To find the resultant of two vectors, you can use the Pythagorean theorem. The components of the vector that you provided are 25 m/s east and 25 m/s north.

Step 1: Draw a diagram to represent the vectors.
- Start at a reference point (usually the origin) and draw the first vector of length 25 m/s to the east.
- From the endpoint of the first vector, draw the second vector of length 25 m/s to the north.

Step 2: Connect the initial point of the first vector to the endpoint of the second vector.

Step 3: Use the Pythagorean theorem to find the length of the resultant vector.
- The Pythagorean theorem states that the square of the length of the hypotenuse (the resultant vector) is equal to the sum of the squares of the lengths of the other two sides.
- In this case, the lengths of the other two sides are 25 m/s (east component) and 25 m/s (north component).
- Therefore, the length of the resultant vector can be found by calculating the square root of (25^2 + 25^2).

Simplifying the equation:

Resultant vector = sqrt(25^2 + 25^2)
= sqrt(625 + 625)
= sqrt(1250)
≈ 35.36 m/s

So, the resultant of the vector with components 25 m/s east and 25 m/s north is approximately 35.36 m/s.