Aledge on a building is 20 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?

 t = 5.4 s

Explanation:

from the question we are given :

height (s) = 20 m

mass of paint (Mp) = 4 kg

mass of nails (Mn) = 3 kg

acceleration due to gravity (g) = 9.8 m/s^{2}

            weight of nails = mass of nails x g = 3 x 9.8 = 29.4 N

            weight of paint = mass nails x g = 4 x 9.8 = 39.2 N

             net force = 39.2 - 29.4 = 9.8 N

             9.8 = (3 +4) x a

              a = 1.4 m/s^{2}

          where U is the initial velocity and is 0 since the can was initially at            

            rest

           20 = (0 x t) + (0.5 x 1.4 x t^{2})

            20 = 0.7 x t^{2}

             t^{2} = 28.6

             t = 5.4 s

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.