Thank you for visiting Find the resultant of two perpendicular vectors whose magnitudes are 54 8 and 39 4 Also find the angle the resultant makes with the 54. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
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.
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Rewritten by : Jeany
