4
QuizMultiple Choice

Modeling with Vector Quantities — Test

Question 4 • Precalculus

A wagon is being pulled by a 300 -pound force that makes a 30 degrees angle with the ground. What are the horizontal and vertical components of the force vector?

Answer
A
The horizontal is 346 pounds, and the vertical is 600 pounds.
B
The horizontal is 600 pounds, and the vertical is 346 pounds.
C
The horizontal is 150 pounds, and the vertical is 260 pounds.
D
The horizontal is 260 pounds, and the vertical is 150 pounds.

Explanation

Since the force makes a 30° angle with the horizontal ground, its horizontal component is 300 cos(30°) ≈ 300(0.866) = 260 pounds. Its vertical component is 300 sin(30°) = 300(0.5) = 150 pounds. Therefore, the horizontal component is 260 pounds and the vertical component is 150 pounds, which is choice D.

AI-written and checked against the verified answer.

Previous
Next