Rock Off Cliff: Greatest Speed?

[eraemia]

Homework Statement

1. A person throws three identical rocks off a cliff of height h with exactly the same speed v0 each time. Rock A is thrown vertically upward, rock B is thrown straight out horizontally, and rock C is thrown straight downward. If we ignore the effects of air resistance, which rock hits the ground with the greatest speed?

a. Rock A
b. Rock B
c. Rock C
d. All rocks hit with the same speed.

2. Consider a ball interacting gravitationally with the earth. Imagine that we choose to define the interaction's potential energy to be zero if the ball is at ground level. A person standing at the bottom of a well throws the ball vertically upward from 20 m below the ground level. The ball makes it all the way up to 1 m below ground level before falling back into the well. The total energy of the ball-earth system is

a. Positive (in this particular case)
b. Positive (because total energy is always positive)
c. Zero
d. Negative
e. The answer depends on the rock's mass
f. Undefined

Homework Equations

The Attempt at a Solution

1. Is it (a), because rock a gets the most time for gravity to accelerate it? Or do all the rocks reach a terminal velocity (but is there terminal velocity without air friction?)?

2. I think that the answer is (d) Negative, because if V(z) = mgz and z < 0, then whatever the mass of the rock is, the potential energy would be zero. But if it asks for the TOTAL energy, do I also include its kinetic energy? In that case, would the TOTAL energy still be negative?

Thanks for the help guys. This forum has helped me a lot as I am taking an introductory physics class, which has a professor who doesn't teach and a textbook that doesn't explain (Six Ideas that Shaped Physics).

 

[learningphysics]

For part 1, think of energies... for each rock... how do the initial energies compare... do they all have the same energy when they are initially thrown?

For part 2, yes it's negative... but why did you say potential energy would be zero? it's negative...

 

[eraemia]

Yeah..I think they all have the same energies when they are thrown. Because kinetic energy only takes into account mass and velocity, which was constant for all three rocks.

But before they fall, when they have potential energy, doesn't the rock with the most height have the most initial potential energy, since V(z) = mgz? So if z is greater, than V(z) would be greater, right? Therefore, isn't the answer to number 1 A, if it has the most energy and speed?

 

[learningphysics]

Yeah..I think they all have the same energies when they are thrown. Because kinetic energy only takes into account mass and velocity, which was constant for all three rocks.

But before they fall, when they have potential energy, doesn't the rock with the most height have the most initial potential energy, since V(z) = mgz? So if z is greater, than V(z) would be greater, right? Therefore, isn't the answer to number 1 A, if it has the most energy and speed?

don't worry about what happens at the maximum height... they all have the same total energy when they hit the ground... they also have the same gravitaitonal potential energies... so what does that tell you about their kinetic energies?

 

[eraemia]

that the kinetic energies are also the same and that the speed of all three rocks are the same

 

[learningphysics]

that the kinetic energies are also the same and that the speed of all three rocks are the same

exactly.

 

[eraemia]

thx for your help, learningphysics

 

[learningphysics]

thx for your help, learningphysics

no prob.