Ronaldo applies a constant force of F⃗ =⟨24,−7⟩ newtons to a box. His brother Federico applies a force −2F⃗ to another heavier box. What is the magnitude and direction of Federico's force? A 34 newtons in the same direction as Ronaldo's force B 34 newtons in a direction opposite to Ronaldo's force C 50 newtons in the same direction as Ronaldo's force D 50 newtons in a direction opposite to Ronaldo's force

9514 1404 393

  D  50 newtons in a direction opposite to Ronaldo's force

Step-by-step explanation:

The factor -2 means the magnitude is doubled and the direction is opposite that of F. We know the magnitude of F is more than 24, so -2F will have a magnitude more than 48. The appropriate choice is ...

  50 newtons in a direction opposite to Ronaldo's force

You can recognize that the components of Ronaldo's force are the smaller numbers of the Pythagorean triple 7-24-25. That recognition tells you the magnitude of Federico's force is 2×25=50 N. Or, you can figure it out using the Pythagorean theorem:

  |Federico's force| = √((-48)² +(14)²) = √(2304 +196) = √2500 = 50