Question

I have this formula that I need to be explained ,please.
It is:
v^2 = 2 gh

Can someone please explain it to me, and maybe give an example problem.

This is not from a quiz or test.
All spammers will be reported promptly.

~CoCo

Answer 1

☺☺Hey mate.....
☺☺See i have proved it in two ways.....plzz check......

☺✌☺✌☺✌☺✌☺✌☺

This is the final speed of an object which falls from a height h with no initial speed to the ground, provided there is no air resistance. So, in this case, it is true.

g is the gravitaitional acceleration of the planet the object is on. Of course, the heavier the planet (or a moon, or a star, or even you) , the bigger g is, so objects fall faster towards it. That is why objects fall much faster on Earth than on the Moon.

There are many ways to prove the formula. I will show there the main two ways.

✔✔✔$ENERGETIC PROOF$

-Since there is no air resistance, the object doesn’t lose or gain energy. So the total energy remains the same.

-At the height h, the object has a potential energy = m * g * h, where m is the mass of the object

-On the ground, the whole potential energy is converted into kinetic energy = (m *v^2) /2

Then, since the total energy is conserved, we have m * g * h = (m * v^2) /2

So, v^2 = 2 * g * h

✔✔✔$KINEMATIC PROOF$

-Because there is no air resistance, every object falls to earth with a constant acceleration g.

-Then, we can know the speed of the object at a given time:

v(t) = g * t (acceleration = speed / t => speed = acceleration * t)

-Also, we can know the total distance an object has covered at a given time:

y(t) = (g * t^2) / 2 (take the average speed, (g * t) / 2 and use distance = average speed * time)

So, we have to solve

v = g * t

h = (g * t * t) / 2 => g * t^2 = 2 * h

Squaring v, we get v ^2 = (g * t) ^ 2 = (g * t^2 ) * g = 2 * h * g

So, v^2 = 2 * g *h

Answer 2

Hey.....here is your answer......☺☺

Ya this formula exist....
KINEMATIC PROOF [/tex]

-Because there is no air resistance, every object falls to earth with a constant acceleration g.

-Then, we can know the speed of the object at a given time:

v(t) = g * t (acceleration = speed / t => speed = acceleration * t)

-Also, we can know the total distance an object has covered at a given time:

y(t) = (g * t^2) / 2 (take the average speed, (g * t) / 2 and use distance = average speed * time)

So, we have to solve

v = g * t

h = (g * t * t) / 2 => g * t^2 = 2 * h

Squaring v, we get v ^2 = (g * t) ^ 2 = (g * t^2 ) * g = 2 * h * g

So, v^2 = 2 * g *h


i hope it helps......you...☺☺☺☺