Vectors and Resultant Forces Flashcards

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

Answer: Distance 10 km, displacement 0 km

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

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

Answer: (0.6, 0.8)

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

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

Answer: About 57.7 N

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

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

Answer: (-10, 0)

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

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

Answer: 30 N

The horizontal component is 50 × 0.6 = 30 N.

As the angle between two forces of fixed size grows from 0° to 180°, what happens to their resultant?

Answer: It decreases steadily

The resultant is largest at 0° (forces add) and smallest at 180° (forces subtract), falling steadily in between.

In a tug-of-war, Team A pulls left with 300 N and Team B pulls right with 250 N. What is the net force on the rope?

Answer: 50 N to the left

Opposite forces subtract, 300 - 250 = 50 N, and the net force points toward the stronger team.