An amusement park ride consists of a rotating circular platform 11.4 m in diameter from which 10 kg seats are suspended at the end of 1.54 m massless chains. When the system rotates, the chains make an angle of 32.3 ◦ with the vertical. What is the speed of each seat?

Explanation:

Formula for horizontal equilibrium is as follows.

Now, we will calculate the radius as follows.

        r =

           =

           = 5.7 m

Also,  

but from the figure r =

So,   r =

          =

          = 6.75 m

Now, we will calculate the velocity as follows.

                   V  =

                     = 8.98 m/s

Thus, we can conclude that the speed of each seat is 8.98 m/s.

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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.