2. A tiny pig is dropped from the top of a building and lands safely on a trampoline. The tiny pig will have

an increase in what type(s) of energy as it falls?

a. Gravity

b. Potential energy

c. Kinetic energy

d. All of the above

c. Kinetic energy

Explanation:

The two types of energy involved in this problem are:

- Potential energy: it is the energy possessed by an object due to its position. It is calculated as

where

m is the mass of the object

g is the acceleration due to gravity

h is the height of the object relative to the ground

From the formula, we see that the higher the object is above the ground (higher h), the larger the potential energy of the object. In this problem, the pig is falling down, so the value of h is decreasing, therefore the potential energy is decreasing as well.

- Kinetic energy: it is the energy possessed by an object due to its motion. It is given by:

where

m is the mass of the object

v is its speed

In this problem, as the pig falls down, it accelerates, so its speed increases: since the kinetic energy is proportional to the square of the speed, as the speed increases, its kinetic energy increases too. So, the correct answer is

c. Kinetic energy

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.