Question

A mouse is trapped in a maze. To find his way out, he walks 15 m, makes a left 90-degree turn, walks 8 m, makes another 90-degree turn, and walks 10 m.

What is the MAGNITUDE of the resultant vector? (round to the nearest tenth)
A) 18.4 m
B) 24.3 m
C) 17.3 m
D) N/A

Answer 1

To find the magnitude of the resultant vector, we break down each displacement into its x and y components, add up the components separately, and use the Pythagorean theorem to find the magnitude.

Step-by-step explanation:

To find the magnitude of the resultant vector, we need to break down each displacement into its x and y components. The first displacement of walking 15 m and making a left 90-degree turn corresponds to a x-component of 0 m and a y-component of -15 m. The second displacement of walking 8 m and making another 90-degree turn corresponds to a x-component of 8 m and a y-component of 0 m. The third displacement of walking 10 m corresponds to a x-component of 10 m and a y-component of 0 m.

Next, we add up the x-components and y-components separately. The resulting x-component is 0 m + 8 m + 10 m = 18 m. The resulting y-component is -15 m + 0 m + 0 m = -15 m.

Finally, we use the Pythagorean theorem to find the magnitude of the resultant vector. The magnitude is sqrt((18 m)^2 + (-15 m)^2) = sqrt(324 m^2 + 225 m^2) = sqrt(549 m^2) ≈ 23.4 m. Therefore, the correct answer is approximately 23.4 m.