Two vectors of magnitudes 25 N and 22 N act at right angles to each other.
What is the magnitude of their resultant?
Answer in units of N
To find the magnitude of the resultant of two vectors acting at right angles to each other, we can use the Pythagorean theorem.
Let's call the vectors A and B, where the magnitude of vector A is 25 N and the magnitude of vector B is 22 N.
According to the Pythagorean theorem, the magnitude of the resultant vector R can be calculated using the formula:
R = √(A^2 + B^2)
Plugging in the values:
R = √(25^2 + 22^2)
Simplifying,
R = √(625 + 484)
R = √1109
R ≈ 33.31 N
Therefore, the magnitude of their resultant is approximately 33.31 N.
To find the magnitude of the resultant vector, we can use the Pythagorean theorem.
The Pythagorean theorem states that for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we can consider the two vectors as the two sides of a right triangle. The magnitude of one vector is 25 N, and the magnitude of the other vector is 22 N. Since the vectors are at right angles to each other, the resultant vector will be the hypotenuse of this right triangle.
Using the Pythagorean theorem, we can calculate the magnitude of the resultant vector:
resultant magnitude^2 = (magnitude of vector 1)^2 + (magnitude of vector 2)^2
resultant magnitude^2 = (25 N)^2 + (22 N)^2
resultant magnitude^2 = 625 N^2 + 484 N^2
resultant magnitude^2 = 1109 N^2
Taking the square root of both sides:
resultant magnitude = √(1109 N^2)
resultant magnitude ≈ 33.32 N
Therefore, the magnitude of the resultant vector is approximately 33.32 N.