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Question
A stone of mass 1.2kg is thrown vertically downwards from a building with an initial speed of 2.0 m/s. The stone loses 96J of gravitational potential energy as it hits the ground. Acceleration due to gravity is 10 m/s. Energy lost due to work done against air resistance is 20J. What is the velocity of the stone just before it hits the ground?

Answer
Hello Isabel,

As I explain this, I will leave some of the math for you to do. At the moment of leaving the top of the building the stone possesses both initial kinetic energy, KEi, due to the throw, and gravitational potential energy, GPEi, due to being at the top of the building. The initial kinetic energy is given by
KEi = (1/2)*m*v^2 = (1/2)*1.2 kg*(2.0 m/s)^2
When you multiply that out, the units of the result will be Joules. The problem says that the stone looses 96 J of GPE on the way down. We can consider ground level to be the reference level, the point at which GPE is zero, so at roof level
GPEi = 96 J.
So the total initial energy,
Eti = KEi + GPEi.

On the way down, the stone looses 20 J of energy due to air resistance. Therefore, as it finally arrives at ground level, the stone's final total energy, Etf, is
Etf = KEi + GPEi - 20 J
The stone has no gravitational potential energy as it reaches the ground, so the stone's total energy, Etf, is entirely kinetic energy, KEf. Therefore KEf and Etf are equal.
So we can say that
KEi + GPEi - 20 J = (1/2)*m*v^2
Plug in the values for KEi, GPEi, and mass, then solve for velocity.

I hope this helps,
Steve
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thank you so much!

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#### Steve Johnson

##### Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

##### Experience

I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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