Respuesta :
Answer:
The recoil velocity of the raft is 1.205 m/s.
Explanation:
given that,
Mass of the swimmer, [tex]m_1=55\ kg[/tex]
Mass of the raft, [tex]m_2=210\ kg[/tex]
Velocity of the swimmer, v = +4.6 m/s
It is mentioned that the swimmer then runs off the raft, the total linear momentum of the swimmer/raft system is conserved. Let V is the recoil velocity of the raft.
[tex]m_1v+m_2V=0[/tex]
[tex]55\times 4.6+210V=0[/tex]
V = -1.205 m/s
So, the recoil velocity of the raft is 1.205 m/s. Hence, this is the required solution.
Answer:
The recoil velocity of the raft would be [tex]v_{r}\approx 1.2\frac{m}{s}[/tex] (pointing to the left if the swimmer runs to the right)
Explanation:
The problem states that the swimmer has a mass of m=55 kg, and the raft has a mass of M=210 kg. Then, it says that the swimmer runs off the raft with a (final) velocity of v=4.6 m/s relative to the shore.
To analyze it, we take a system of "two particles", wich means that we will consider the swimmer and the raft as a hole system, aisolated from the rest of the world.
Then, from the shore, we can put our reference system and take the initial moment when the swimmer and the raft are stationary. This means that the initial momentum is equal to zero:
[tex]p_{i}=0[/tex]
Besides, we can use magnitudes instead of vectors because the problem will develope in only one dimension after the initial stationary moment (x direction, positive to the side of the running swimmer, and negative to the side of the recoling raft), this means that we can write the final momentum as
[tex]p_{f}=mv-Mv_{r}=0[/tex]
The final momentum is equal to zero due to conservation of momentum (because there are no external forces in the problem, for the system "swimmer-raft"), so the momentum is constant.
Then, from that previous relation we can clear
[tex]v_{r}=\frac{m}{M}v=\frac{55}{210}*4.6\frac{m}{s}=\frac{253}{210}\frac{m}{s}\approx1.2\frac{m}{s}[/tex]
wich is the recoil velocity of the raft, and it is pointing to the left (we established this when we said that the raft was going to the negative side of the system of reference, and when we put a minus in the raft term inside the momentum equation).
