How Do Speeds Change After an Elastic Collision?

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In a perfectly elastic collision, both momentum and kinetic energy are conserved. To find the speeds of balls A and B after the collision, the equations for conservation of momentum and kinetic energy must be applied. For ball A, the final speed can be calculated using the formula derived from these conservation principles, which takes into account the masses and initial velocities of both balls. Similarly, the final speed of ball B can be determined using the same principles. Understanding these calculations is crucial for solving the problem accurately.
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Ball A, a 0.055 kg ball, moving with a speed of 2.50 m/s collides head-on with ball B, a 0.095 kg ball initially moving away from it at a speed of 1.15 m/s. Assume a perfectly elastic collision. Take the initial velocity of ball A to be in the positive x direction.

(A) What is the speed of ball A after the collision?

(B) What is the speed of ball B after the collision

Can anyone walk me through this? I'm not sure where to start...
 
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Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
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