Question

A vector has a magnitude of 15 meters at a direction of 40 degrees. What are the horizontal and vertical components of the vector?

A) Horizontal component: 11.47 meters, Vertical component: 9.65 meters
B) Horizontal component: 9.65 meters, Vertical component: 11.47 meters
C) Horizontal component: 12.34 meters, Vertical component: 8.76 meters
D) Horizontal component: 8.76 meters, Vertical component: 12.34 meters

Answer 1

The horizontal and vertical components of a vector with a magnitude of 15 meters at a direction of 40 degrees can be calculated as approximately 11.47 meters and 9.65 meters, respectively, making the correct answer A.

Step-by-step explanation:

To find the horizontal and vertical components of a vector with magnitude and direction, you can use trigonometric functions. For a vector with a magnitude of 15 meters at a direction of 40 degrees:

• The horizontal component (x) can be found using cosine: x = magnitude * cos(angle), which is x = 15 * cos(40°).
• The vertical component (y) can be found using sine: y = magnitude * sin(angle), which is y = 15 * sin(40°).

When calculated, this gives:

• Horizontal component: 11.49 meters (approximately 11.47 meters)
• Vertical component: 9.64 meters (approximately 9.65 meters)

Therefore, the correct answer is A) Horizontal component: 11.47 meters, Vertical component: 9.65 meters based on standard rounding rules.