Question

(e) The energy of a moving object is directly proportional to the square of its speed.
The speed of the object is increased by 30%.
Calculate the percentage increase in the energy of the object.

Answer 1

We will see that the energy is increased by 69%.

How to find the percentage increase in the energy?

First, we know that the energy is proportional to the square of the speed, so we can write:

E = k*v^2

Where k is the constant of proportionality.

Now, if we increase the velocity by 30%, then the new velocity will be:

v' = (1 + 0.3)*v = 1.3*v

Replacing that in the energy, we get the new energy:

E' = k*(1.3*v)^2 = k*(1.3)^2*(v)^2

E' = (k*v^2)*(1.3)^2 = (k*v^2)*1.69

And the first parenthesis is equal to the original energy, so we can write:

E' = E*1.69 = E*1.69

To get the percentage increase, we just multiply the factor by 100%, and then subtract 100%, we will get:

1.69*100% - 100% = 169% - 100% = 69%

Thus, the percentage increase in the energy of the object is 69%.

If you want to learn more about percentages, you can read:

https://brainly.com/question/843074