The acceleration of gravity is 9.81 m/s 2 . If a 56.4 g egg falls 14.0 m from rest and the 7.85 cm thick foam pad stops it in 6.05 ms, by how much is the pad compressed? Assume constant upward acceleration as the egg compresses the foam-rubber pad.

The pad is compressed by 5.02 cm

Explanation:

First of all, we have to calculate the initial mechanical energy of the egg, which is equal to its gravitational potential energy at the top:

where

is the mass of the egg

is the acceleration due to gravity

h = 14.0 m is the initial height

Substituting

As the egg falls down, this energy is conserved and it is entirely converted into kinetic energy; so, when the egg reaches the pad, its energy is now equal to its kinetic energy:

where

u is the velocity of the egg as it reaches the pad

Solving for u,

Then, the egg is stopped by the pad, so it has a uniformly accelerated motion; so we can find the distance it takes to stop by using the  suvat equation

where:

u = 16.6 m /s is the initial velocity

v = 0 is the final velocity

is the stopping time

Solving,

So, the pad is compressed by 5.02 cm.

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.

ok

explanation: