To solve for the speed of the raft after the swimmer dives off, we can use the principle of conservation of momentum. Before the diver jumps, both the swimmer and the raft are at rest, so the total initial momentum is zero.
Let:
- Mass of the swimmer (m₁) = 75 kg
- Velocity of the swimmer (v₁) = 4 m/s (after jumping)
- Mass of the raft (m₂) = 500 kg
- Velocity of the raft (v₂) = ? (this is what we are trying to find)
According to the conservation of momentum:
\[ (m₁ + m₂) \cdot 0 = m₁ \cdot v₁ + m₂ \cdot v₂ \]
This simplifies to:
\[ 0 = (75 \text{ kg} \cdot 4 \text{ m/s}) + (500 \text{ kg} \cdot v₂) \]
Calculating the momentum of the swimmer:
\[ 0 = 300 \text{ kg m/s} + 500 \text{ kg} \cdot v₂ \]
Now, we can solve for \( v₂ \):
\[ 500 \text{ kg} \cdot v₂ = -300 \text{ kg m/s} \]
\[ v₂ = -\frac{300 \text{ kg m/s}}{500 \text{ kg}} \]
\[ v₂ = -0.6 \text{ m/s} \]
The negative sign indicates that the raft moves in the opposite direction to the swimmer. Thus, the speed of the raft is 0.6 m/s.
Based on the provided options, the correct answer is:
c 0.6 m/s