31kg.swimmer.runs.with.a.horizontal..velocity.of.4,0.m/s.off.a.boat.dock.and.lands.in.a.stationery.rubber.raft.of.mass.og.9kg..what.would.be.the.velocity.of.the.swimmer.and.raft.after.the.impact.assuming.no.water.resistance
To determine the velocity of the swimmer and raft after the impact, we can use the principle of conservation of momentum. According to this principle, the total momentum before the impact is equal to the total momentum after the impact, assuming no external forces act on the system.
The momentum of an object is given by the product of its mass and velocity (p = m * v).
Let's denote the velocity of the swimmer as V1, the velocity of the raft as V2, the mass of the swimmer as m1 (31 kg), and the mass of the raft as m2 (9 kg).
Before the impact:
The swimmer is running with a horizontal velocity of 4.0 m/s. Since the swimmer is at rest vertically (stationary), the initial vertical velocity is 0 m/s. Thus, the initial momentum of the swimmer is: p1 = m1 * 4.0.
The raft is stationary, so its initial velocity is 0 m/s. Therefore, the initial momentum of the raft is: p2 = m2 * 0.
Total initial momentum: p_initial = p1 + p2.
After the impact:
By the conservation of momentum, the total momentum after the impact should be equal to the total initial momentum.
Since the swimmer and the raft are now moving as a combined system, their final momentum can be calculated as the sum of their individual momenta: p_final = (m1 + m2) * V_final.
Setting the initial and final momenta equal to each other, we have:
p1 + p2 = (m1 + m2) * V_final.
Substituting the given values:
m1 = 31 kg, m2 = 9 kg, p1 = m1 * 4.0, p2 = m2 * 0.
(31 * 4.0) + (9 * 0) = (31 + 9) * V_final.
124 + 0 = 40 * V_final.
124 = 40 * V_final.
Now, we can solve for V_final:
V_final = 124 / 40.
V_final = 3.1 m/s.
Therefore, the velocity of the swimmer and raft after the impact, assuming no water resistance, would be 3.1 m/s.