AT WHAT HIGHT ABOVE THE GROUND MUST A BODY OF MASS 10KG IS SITUATED IN OTHER TO HAVE POTENTIAL ENERGY EQUAL IN VALUE TO THE KINETIC ENERGY POSSESSED BY ANOTHER BODY OF MASS 10KG MOVING WITH A VELOCITY OF 10M/S
The height Of calmness!
1/2 * m*10^2=m*9.8*h
solve for h: h=50/9.8 meters
To solve this problem, we need to equate the gravitational potential energy of the stationary body to the kinetic energy of the moving body. Let's break it down step by step.
The potential energy (PE) of an object at a certain height above the ground is given by the formula:
PE = m * g * h
Where:
m is the mass of the object (10 kg),
g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth),
h is the height above the ground.
The kinetic energy (KE) of an object in motion is given by the formula:
KE = (1/2) * m * v^2
Where:
m is the mass of the object (10 kg),
v is the velocity of the object (10 m/s).
Now, let's equate the two energies:
PE = KE
m * g * h = (1/2) * m * v^2
Since the mass (m) is common on both sides of the equation and cancels out, we can simplify further:
g * h = (1/2) * v^2
Plugging in the values, we have:
(9.8 m/s^2) * h = (1/2) * (10 m/s)^2
Simplifying:
9.8h = 0.5 * 100
9.8h = 50
Now, we can solve for h by dividing both sides by 9.8:
h = 50 / 9.8
h ≈ 5.10 meters
Therefore, the stationary body must be situated at a height of approximately 5.10 meters above the ground to have potential energy equal in value to the kinetic energy possessed by the moving body.