How Quickly Can a Rock Be Hoisted with Limited String Strength?

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SUMMARY

The minimum time to hoist a 1.00-kg rock to a height of 10.0 meters using a string with a breaking strength of 10.8 N is calculated to be 4.5 seconds. The formula used is derived from the equation of motion, specifically a=2(x-xo)/t^2, leading to the conclusion that t equals the square root of 10.8. Additionally, if the string's strength is increased by 50%, the time required to hoist the rock will be reduced by a specific percentage, which can be determined once the initial time is established.

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a) What is the minimum time in which one can hoist a 1.00-kg rock height of 10.0m if the string used to pull the rock up has a breaking strength of 10.8 N? Assume the rock to be initially at rest.


b) If the string is replaced by one that is 50% stronger, by what percentage will the minimum time for the hoist be reduced.


a)

i just used a= 2(x-xo)/t^2 and then i got 2(10)/t^2 = 10.8/1
so i got 10.8=20/t^2 and so t would be root 10.8 but the answer is 4.5seconds... how?



b) i need to get a) to solve this...
 
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Hint 1: Draw a free body diagram for the rock.
Hint 2: There is some provided info in the problem you haven't used yet.
 

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