A vector of magnitude 3.8 directed along the positive x-axis combines with a second vector directed along the positive y-axis to produce a total vector of magnitude 6.1. What is the magnitude of the second vector?
A) 2.7
B) 9.5
C) 23.5
D) 4.8
E) Not enough information is given.

Question

Quizplus · Accepted Answer

We can use the Pythagorean theorem to solve this problem. Let's call the magnitude of the second vector "y".

We know that the total vector has a magnitude of 6.1, so:

6.1² = 3.8² + y²

Simplifying:

37.21 = 14.44 + y²

Subtracting 14.44 from both sides:

22.77 = y²

Taking the square root of both sides (and remembering that we only care about the positive root, since y is a magnitude):

y ≈ 4.8

So the magnitude of the second vector is approximately 4.8. The answer is D.

A Vector of Magnitude 3