Solve Time to Pull Illinois Jones from Pit

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To determine the minimum time to pull Illinois Jones from the pit, the tension in the rope must be considered alongside gravitational force. The net force acting on him is the difference between the tension (725 N) and the weight (approximately 607.2 N). This results in a net force of about 117.8 N, leading to an acceleration of approximately 1.9 m/s². Using this acceleration, the time can be calculated based on the depth of the pit (3.9 m) and the kinematic equations. The calculations indicate that the initial approach to finding acceleration was flawed due to neglecting the gravitational force.
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Illinois Jones is being pulled from a snake pit with a rope that breaks if the tension in it exceeds 725 N. If Illinois Jones has a mass of 62 kg and the snake pit is 3.9 m deep, what is the minimum time necessary to pull our intrepid explorer from the pit?



F=ma and a=d/t^2



I put in 725 for the force so I had 725=(62kg)(a) and that gave me 11.69 for a, but that doesn't really make sense. That may be right but seems like an insanely high acceleration. Was I wrong in doing that?
 
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The acceleration is produced by the net force. The tension in the rope is not the only force acting on him.
 

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