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  4. A little boy having mass 15 kg climbing on a rope with one end fixed to the ceiling. If it wishes to go up with an acceleration of 1 m text/s2 and rope is 5m long, also monkey starts from roof then how much time will it take to reach the ceiling? (take g = 10 m text/s2 )

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Q. A little boy having mass 15 kg climbing on a rope with one end fixed to the ceiling. If it wishes to go up with an acceleration of $ 1\,\,m\text{/}{{s}^{2}} $ and rope is 5m long, also monkey starts from roof then how much time will it take to reach the ceiling? (take g = 10 $ m\text{/}{{s}^{2}} $ )

CMC MedicalCMC Medical 2015

Solution:

Given, mass m = 15 kg acceleration, $ a=1\,m/{{s}^{2}} $ and initial velocity, $ u=0 $ As the length of rope is 5 m. So, height attained by child in given as $ s=ut+\frac{1}{2}a{{t}^{2}} $ $ \Rightarrow $ $ 5=0+\frac{1}{2}\times 1\times {{t}^{2}}\Rightarrow {{t}^{2}}=5\times 2 $ or, $ t=\sqrt{10}\,s $