Question

In a game of tug-of-war, a team wins by pulling the flag over its goal line. The flag begins at 0. During a game, the flag moves 8 feet to the right, 12 feet to the left, and 13 feet back to the right. Did a team win? Explain

Answer 1

Yes, a team won. The flag's net displacement was 9 feet in the positive direction.

Step-by-step explanation:

In order to determine if a team won in a game of tug-of-war, we need to calculate the net displacement of the flag. Let's consider the flag's movements:

1. Moves 8 feet to the right (+8 feet)
2. Moves 12 feet to the left (-12 feet)
3. Moves 13 feet to the right (+13 feet)

To calculate the net displacement, we add up the displacements: +8 feet -12 feet +13 feet = 9 feet. Since the flag has a positive net displacement of 9 feet, it crossed over the goal line and the team won.

Answer 2

Think of the flag as 0 on a number line. Move to the right is positive, move to the left is negative...

We begin on 0 and move 8 feet to the right. Now we move 12 feet to the left... 8 - 12 = -4. We are at -4 on the number line. Now we move back to the right 13 feet... -4 + 13 = 9. We are at 9 on the number line.

So did any team win? It depends on how far the goal line is from zero. We know that it's farther than 8 feet from zero because they didn't call the game after the first 8 feet. When it went back to the left it only went 4 feet from zero. When it goes back to the right, it is now 9 feet from zero. If the goal line is 9 feet or less from zero then one of the teams win... but if the goal line is greater than 9 feet from 0, no team wins (because nobody went that far).

Don't worry... I'm sure that both teams got a participation ribbon. . .