A 60-kg swimmer dives from a 150-kg raft with a horizontal speed of 1.5 m/s. The raft is initially at rest. What is the speed of the raft immediately after the diver jumps?

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BlackTom AI · Accepted Answer

Momentum conservation in the horizontal direction is the key to this problem. The system consists of the swimmer and the raft, and there are no external horizontal forces, so the total horizontal momentum before and after the jump must be the same.

Option A: 0.6 m/s. If the diver has a horizontal speed of 1.5 m/s relative to the ground after jumping, the swimmer contributes momentum 60 kg × 1.5 m/s = 90 kg·m/s to the system. To balance this, the raft (150 kg) must have momentum -90 kg·m/s, which corresponds to a raft speed of v = -90 / 150 = -0.6 m/s (direction opposite to the diver’s motion). The magnitude is 0.6 m/s, so this option is consistent with momentum conservation.

Option B: None of these. Given the straightforward momentum calculation with the provided numbers, one specific speed magnitude emerges (0.6 m/s). It would be unusual if none matched the correct balance, so this option is unlikely unless there is a misinterpretation of the given speeds.

Option C: 1.1 m/s. If the raft were to move at 1.1 m/s, its momentum would be 150 kg × 1.1 m/s = 165 kg·m/s in the positive direction, which would require the diver to have negative momentum of -165 kg·m/s to conserve momentum. That would imply a diver speed of -165 / 60 ≈ -2.75 m/s, contradicting the given diver speed of +1.5 m/s. Hence this option does not satisfy momentum conservation with the stated numbers.

Option D: 0.8 m/s. A raft speed of 0.8 m/s would give raft momentum 150 × 0.8 = 120 kg·m/s in the positive direction. The diver would then need momentum -120 kg·m/s, which requires a diver speed of -120 / 60 = -2.0 m/s. This conflicts with the given diver speed of +1.5 m/s, so this option is incorrect.

Option E: 0.19 m/s. If the raft moved at 0.19 m/s, its momentum would be 150 × 0.19 ≈ 28.5 kg·m/s. The diver would need momentum -28.5 kg·m/s, implying a diver speed of -28.5 / 60 ≈ -0.475 m/s, again not matching the stated 1.5 m/s for the diver. Therefore this option does not align with the given information.

Across the options, only the combination of diver speed 1.5 m/s and raft mass 150 kg with diver mass 60 kg leads to a raft speed of 0.6 m/s in the opposite direction when applying momentum conservation. The other speeds fail to satisfy the momentum balance with the provided speeds and masses.

2025 Fall PHYS 2205 TR 11:00 - 12:15 _ 89122 2205 Final Exam

A 60-kg swimmer dives from a 150-kg raft with a horizontal speed of 1.5 m/s. The raft is initially at rest. What is the speed of the raft immediately after the diver jumps?

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