Answer :
The resultant of two perpendicular vectors with magnitudes of 54.8 and 39.4 is approximately 67.5, and it makes a 36.0° angle with the 54.8 vector.
To find the resultant of two perpendicular vectors with magnitudes of 54.8 and 39.4, we can use the Pythagorean theorem. The resultant vector (
) can be found by taking the square root of the sum of the squares of the two vector magnitudes
= √(54.8² + 39.4²) = √(3002.44 + 1552.36) = √(4554.8) ≈ 67.5
The angle ( heta) the resultant makes with the 54.8 vector (which can be considered the adjacent side in a right triangle) can be found using the arctan function, which gives:
heta = arctan(39.4/54.8) ≈ 36.0°
Thus, the resultant vector's magnitude is approximately 67.5, and it makes a 36.0° angle with the 54.8 vector.
