Three way tug of war vectors | Vectors | Precalculus | Khan Academy

TL;DR

Team B will win the tug of war game because they are pulling with the greatest magnitude in their direction.

Transcript

Voiceover: Teams A, B, and C are playing a game of strength. Each team has attached a rope to a metal ring and is trying to pull the ring into their own area. Team areas shown below. Let's see what that's ... We see that over here team A is pulling on the ring in that direction. Team B is pulling on the ring in that direction. Team C is pulling on ... Read More

Key Insights

• 🏆 Team B will win the tug of war game due to the greater magnitude of their force vector.
• ❓ The magnitude of a force vector can be determined by using the Pythagorean theorem.
• 😋 The combined force acting on the ring is the sum of the individual force vectors.
• ❓ The magnitude of the combined force vector can be found using the Pythagorean theorem.

Questions & Answers

Q: Which team will win the game and why?

Team B will win the game because the magnitude of their force vector (-2i + 4j) is greater than the magnitudes of the force vectors of teams A and C.

Q: What is the magnitude of Team A's force vector?

The magnitude of Team A's force vector is 4 kilo newtons, as it is a multiple of the unit vector i.

Q: How do we determine the magnitude of Team B's force vector?

We can use the Pythagorean theorem to find the magnitude of Team B's force vector. It is equal to the square root of (-2^2 + 4^2), which is the square root of 20.

Q: How do we know that Team C's force vector has a larger magnitude than Team A's?

We compare the magnitudes of Team A's force vector (4) and Team C's force vector (square root of 18). Since the square root of 20 is larger than 4, Team C's force vector has a larger magnitude.

Q: What is the magnitude of the teams' combined forces acting on the ring?

The magnitude of the combined force vector is the square root of 2, which is approximately 1.4 kilo newtons.

Q: In what direction is the ring getting pulled?

The ring is getting pulled in the direction represented by the force vector -i + j. This direction corresponds to an angle of approximately 2.4 radians.

Summary & Key Takeaways

• Teams A, B, and C are competing in a game of strength, trying to pull a metal ring into their respective areas.

• Team A pulls with a force vector of 4 times the unit vector i (positive x direction).

• Team B pulls with a force vector of -2i + 4j (left and up direction).

• Team C pulls with a force vector of -3i - 3j.