Finding displacement with acc and vel

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The discussion revolves around calculating the maximum height a lighter object can achieve in a pulley system after a heavier object hits the ground. The initial positions of both objects are 0.3 m above ground with zero initial velocity. The user has determined that the lighter object will be lifted by 0.3 m due to the heavier object's fall, resulting in a height of 0.6 m. The challenge lies in calculating the additional height gained from momentum while considering the downward acceleration due to gravity. The user is advised to apply the principle of conservation of energy to solve the problem effectively.
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I'm working on a problem involving pulleys and would appreciate help. I know the initial starting positions of both objects (0.3 m above ground) and their initial velocity which is zero. The question wants me to find the maximum height the lighter object can achieve - i.e. its height even after the heavier object hits the ground, since it will be carried upwards by momentum. I have worked out the velocity of both objects, which are same magnitude and opposite directions, through equating kinetic energy and work done by gravity (since I know both their masses). I can also presume that, when the heavier object hits the ground, the lighter would have been lifted up by 0.3m, making it a total of 0.6m. I am just having problems with the additional height the lighter object travels through momentum, since I need to take into account the downward acceleration by gravity. (I am not given any information regarding time). Any advice on how to approach this would be appreciated.
 
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Hint: conservation of energy.
 
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