BMST Vectors and Resultant Forces 5

Question 1

A hiker walks 5 km north and then 5 km south. What are the hiker's distance traveled and displacement?

Accepted Answer

Distance 10 km, displacement 0 km

Answer

Distance adds up the whole path, but the displacement is zero because the hiker ends where they started.

Question 2

What is the unit vector in the direction of (3, 4)?

Accepted Answer

(0.6, 0.8)

Answer

Divide each component by the magnitude 5 to get (3/5, 4/5) = (0.6, 0.8).

Question 3

A 100 N sign hangs from two identical ropes, each at 60° above the horizontal. What is the tension in each rope?

Accepted Answer

About 57.7 N

Answer

The vertical parts must balance the weight: 2T sin 60° = 100 N, so T ≈ 57.7 N.

Question 4

A vector of magnitude 10 points at 180° from the positive x-axis. What are its components?

Accepted Answer

(-10, 0)

Answer

x = 10 cos 180° = -10 and y = 10 sin 180° = 0.

Question 5

A 50 N force acts at an angle where cos θ = 0.6 and sin θ = 0.8. What is its horizontal component?

Accepted Answer

30 N

Answer

The horizontal component is 50 × 0.6 = 30 N.

BMST - Basic Math and Science Test Practice Test