A 73-kg swimmer dives horizontally off a 500-kg raft. The diver's speed immediately after leaving the raft is 5.0 m/s. A micro-sensor system attached to the edge of the raft measures the time interval during which the diver applies an impulse to the raft just prior to leaving the raft surface. If the time interval is read as 0.20 s, what is the magnitude of the average horizontal force by diver on the raft?Select one:a.365 Nb.1,825 Nc.73 Nd.2,500 Ne.25 N
Question
A 73-kg swimmer dives horizontally off a 500-kg raft. The diver's speed immediately after leaving the raft is 5.0 m/s. A micro-sensor system attached to the edge of the raft measures the time interval during which the diver applies an impulse to the raft just prior to leaving the raft surface. If the time interval is read as 0.20 s, what is the magnitude of the average horizontal force by diver on the raft?Select one:a.365 Nb.1,825 Nc.73 Nd.2,500 Ne.25 N
Solution
To solve this problem, we need to use the concept of momentum conservation. The total momentum before the diver jumps is zero (since both the diver and the raft are initially at rest). The total momentum after the diver jumps must also be zero (since there are no external forces).
The momentum of the diver after he jumps is his mass times his velocity, which is 73 kg * 5.0 m/s = 365 kg*m/s.
Since the total momentum must be conserved, the momentum of the raft must be -365 kg*m/s (it moves in the opposite direction of the diver).
The impulse applied to the raft is the change in its momentum, which is -365 kgm/s - 0 = -365 kgm/s.
Impulse is also equal to the average force applied times the time interval, so we can set up the equation -365 kg*m/s = F_avg * 0.20 s.
Solving for F_avg gives us F_avg = -365 kg*m/s / 0.20 s = -1825 N.
The negative sign indicates that the force is in the opposite direction of the diver's motion, but since the question asks for the magnitude of the force, we can ignore the sign.
So, the magnitude of the average horizontal force by the diver on the raft is 1825 N.
Therefore, the correct answer is (b) 1,825 N.
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