A stone of mass 0.55 kilograms is released and falls to the ground. Measurements show that the stone has a kinetic energy of 9.8 joules at the point of impact with the ground. What is the stone's velocity when it hits the ground?
7.2
you figure it out
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To find the stone's velocity when it hits the ground, we first need to determine its initial gravitational potential energy and its final kinetic energy.
First, let's determine the initial gravitational potential energy:
The potential energy of an object near the surface of the Earth is given by the equation:
Potential Energy = mass × acceleration due to gravity × height
In this case, the stone is released, so its initial height is zero. Thus, the initial potential energy is zero.
Next, let's determine the final kinetic energy:
The kinetic energy of an object is given by the equation:
Kinetic Energy = 1/2 × mass × velocity^2
We are given that the final kinetic energy is 9.8 joules.
Now, let's plug in the values we know into the equation:
9.8 joules = 1/2 × 0.55 kilograms × velocity^2
Dividing both sides of the equation by 0.55 kilograms:
9.8 joules / 0.55 kilograms = 1/2 × velocity^2
Simplifying the equation:
17.8182 joules/kilogram = velocity^2
Finally, taking the square root of both sides of the equation gives us the stone's velocity when it hits the ground:
velocity = √(17.8182 joules/kilogram) = 4.22 m/s
Therefore, the stone's velocity when it hits the ground is 4.22 m/s.