To find the velocity of an object when its mass and height are given, you can use the concept of gravitational potential energy and kinetic energy. Here’s how it works:
When an object is at a certain height, it possesses gravitational potential energy (PE) calculated with the formula:
PE = m * g * h
where:
- m = mass of the object (in kilograms),
- g = acceleration due to gravity (approximately 9.81 m/s² on Earth), and
- h = height (in meters).
As the object falls, this potential energy converts into kinetic energy (KE), given by the formula:
KE = 0.5 * m * v²
where:
- v = velocity of the object (in meters per second).
At the point of falling, when all the potential energy has transformed into kinetic energy, we can equate the two:
m * g * h = 0.5 * m * v²
The mass (m) cancels out from both sides, simplifying to:
g * h = 0.5 * v²
Now, we can solve for v:
v² = 2 * g * h
v = sqrt(2 * g * h)
So, if you have the mass and height, you can find the velocity at the point of impact by plugging in the values for g and h into the formula. This gives you the speed of the object just before it hits the ground!