Question

1. dylan and hunter are pushing a box toward each other. on a scale of 1 to 10, dylan is pushing at a 6 and hunter is pushing at an 8. which statement below is not true? a. the box will move away from hunter. b. the box will move toward dylan. c. the force is balanced. d. if dylan began pushing at an 8, the box would stop moving.

Explanation:

1. Analyze the forces: Dylan pushes with a force of 6, Hunter with 8. Since forces are in opposite directions (pushing toward each other), the net force is \(8 - 6 = 2\) in Hunter's direction (or away from Dylan, toward Hunter? Wait, no—wait, if they push toward each other, Dylan's force is, say, to the right (toward Hunter) and Hunter's to the left (toward Dylan)? Wait, no, the problem says "pushing a box toward each other"—so Dylan is pushing the box toward Hunter, and Hunter is pushing the box toward Dylan. So their forces are opposite. So the magnitude of Hunter's force (8) is greater than Dylan's (6). So the net force is \(8 - 6 = 2\) in the direction Hunter is pushing (toward Dylan? Wait, no: if Dylan pushes the box toward Hunter (so force vector from Dylan to Hunter), and Hunter pushes the box toward Dylan (force vector from Hunter to Dylan), then the two forces are opposite. So the net force is \(8 - 6 = 2\) in the direction of Hunter's force (toward Dylan? Wait, no—if Dylan is pushing the box toward Hunter (so the box would move toward Hunter if only Dylan pushed), and Hunter is pushing the box toward Dylan (so the box would move toward Dylan if only Hunter pushed). Since Hunter's force (8) is stronger than Dylan's (6), the net force is toward Dylan (because Hunter's force is stronger, so the box moves in the direction of Hunter's push, which is toward Dylan). Wait, maybe I got the direction wrong. Let's rephrase:

• Dylan's force: pushing the box toward Hunter (so force vector: Dylan → Box → Hunter)
• Hunter's force: pushing the box toward Dylan (so force vector: Hunter → Box → Dylan)

So the two forces are opposite. The magnitude of Hunter's force (8) is greater than Dylan's (6). So the net force is \(8 - 6 = 2\) in the direction of Hunter's force (toward Dylan). So the box will move toward Dylan (so B is true), which means it moves away from Hunter (so A is true? Wait, no—if it moves toward Dylan, it's moving away from Hunter. Wait, Dylan and Hunter are pushing toward each other, so the box is between them. If the box moves toward Dylan, it's moving away from Hunter. So A: "The box will move away from Hunter"—if it moves toward Dylan, yes, that's true. B: "The box will move toward Dylan"—true, because net force is toward Dylan. C: "The force is balanced"—balanced forces have equal magnitude. Here, 6 ≠ 8, so forces are unbalanced. So C is not true. D: "If Dylan began pushing at an 8, the box would stop moving"—if Dylan pushes at 8 and Hunter at 8, then net force is \(8 - 8 = 0\), so balanced forces, box stops. So D is true. Therefore, the statement that is NOT true is C.

Answer:

C. The force is balanced.