Question

A body moves with a displacement of 12 m east, 5 m north, and 9 m vertically upwards. What is the magnitude of its resultant displacement?

A. 15 m
B. 16 m
C. 20 m
D. 22 m

Answer 1

The magnitude of the resultant displacement is approximately 15.81 m.

Step-by-step explanation:

To find the magnitude of the resultant displacement, we can use the Pythagorean theorem. The displacement in the east-west direction is 12 m, in the north-south direction is 5 m, and in the vertical direction is 9 m. Let's call the east-west direction the x-axis, the north-south direction the y-axis, and the vertical direction the z-axis.

Using the Pythagorean theorem, we can calculate the magnitude of the resultant displacement:

R = sqrt((12)^2 + (5)^2 + (9)^2) = sqrt(144 + 25 + 81) = sqrt(250)

To simplify the square root, we can factor out 25:

R = 5 * sqrt(10)

Therefore, the magnitude of the resultant displacement is approximately 15.81 m. So, the correct answer is option A. 15 m.