Two diamonds begin a free fall from rest from the same height 0.9 s apart. How long after the first object begins to fall will the two objects be 13 m apart

Explanation:

Suppose the first diamond falls for t seconds

The downward displacement S₁ = u t + g t²

here u = 0 , because it was at rest initially

Thus S₁ = g t²              I

Similarly second diamond moves for time ( t - 0.9 ) sec

The distance covered by it is

S₂ = g (t - 0.9 )²

The separation between the two is 13 m

Thus S₁ - S₂ = 13 m

g t² - g t² + 0.9 g t - 0.4 g = 13

or  9 t = 13 - 4 = 9

Hence t = 1 sec

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.

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.