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A ledge on a building is 18 m above the ground. A taut rope attached to a 4.0-kg can of paint sitting on the ledge passes up over a pulley and straight down to a 3.0-kg can of nails on the ground.If the can of paint is accidently knocked off the ledge, what time interval does a carpenter have to catch the can before it smashes on the floor?

Respuesta :

Answer:t=5.07 s

Explanation:

Given

height of Building h=18 m

mass of Paint can [tex]m_1=4 kg[/tex]

mass of second can [tex]m_2=3 kg[/tex]

let T be the Tension in the rope

For  4 kg can

[tex]4g-T=4a[/tex]

[tex]T=4(g-a)[/tex]----1

For 3 kg can

[tex]T-3g=3a[/tex]

[tex]T=3(g+a)[/tex]----2

From 1 and 2

[tex]4(g-a)=3(g+a)[/tex]

[tex]g=7a[/tex]

[tex]a=\frac{g}{7}[/tex]

So time taken to cover 18 m is

[tex]h=ut+\frac{at^2}{2}[/tex]

[tex]18=0+\frac{g\cdot t^2}{7\times 2}[/tex]

[tex]t^2=\frac{18\times 2\times 7}{g}[/tex]

[tex]t=5.07 s[/tex]

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