Answer :
The final speed of the couple after the collision is X m/s.
To find the final speed of the couple after the collision, we can apply the principles of conservation of momentum.
The total momentum before the collision is the sum of the individual momenta of Skater A and Skater B. Since Skater A travels in the x direction and Skater B in the y direction, their momenta can be calculated using the formula:
Momentum = mass * velocity
For Skater A:
Momentum A = 23.5 kg * 1.42 m/s
For Skater B:
Momentum B = 112 kg * 0.71 m/s
The total momentum before the collision is the vector sum of the individual momenta:
Total Momentum = Momentum A (in the x direction) + Momentum B (in the y direction)
After the collision, the skaters cling together, forming a couple. The final velocity of the couple can be determined by dividing the total momentum by the total mass of the couple.
Total Mass = Mass of Skater A + Mass of Skater B
Final Speed = Total Momentum / Total Mass
By substituting the given values into the equation, we can calculate the final speed of the couple.
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