Final velocity of a rock and how it compares to work

[ja!mee]

Homework Statement

I have been given this example with the following questions:
1. Two rocks are thrown off of a cliff with the same initial speed, v. The first rock is launched with at an angle Ө directed below the horizontal as shown below as 1, while the second rock is launched above at the same angle.
a. Predict how the final speeds of each rock compare just before they strike the water. Provide a brief explanation justifying your prediction.

b. Measurements are taken and it turns out that both rocks strike the water below at precisely the identical speed. Justify using a conservation of energy argument. Use equations to aid your explanation.

c. Justify using a kinematics argument (projectile motion). The diagram below might help your explanation.

( I attached the two diagrams provided)

Homework Equations

This is where I am getting messed up... The unit that this question belongs to is in the Work, energy, power, and efficiency portion of my course work... I am under the impression that this is a kinematics question... I can't seem to see how this fits into Work, energy, power or efficiency. As none of these things are even mentioned.

The Attempt at a Solution

a. Predict how the final speeds of each rock compare just before they strike the water. Provide a brief explanation justifying your prediction.

I do know that they will strike the water at the same time, I am just unsure how to justify this in terms of work, energy, power, or efficiency.

Thats about as far as I've gotten, I have been staring at it for ever and I just can't seem to make it click... any explanation would be helpful

 

[tiny-tim]

hi ja!mee!

I do know that they will strike the water at the same time, I am just unsure how to justify this in terms of work, energy …

hint: what are the forces on it?

are they conservative?

 

[Nugatory]

1
I do know that they will strike the water at the same time

Is that what the problem says?

 

[ja!mee]

okay ... so

a) The angle of the projectile does not matter since the angle does not change the amount of energy that the rock possesses.

b) and to justify the conservation of energy would be:
The sum of the potential and kinetic energy at launch is:

E_i = PE +KE - mgh_cliff + 1/2mv₁²

At the water all of the energy would be kinetic so:
E_f = KE = 1/2mv_f²

and since energy is conserved throughout:
mgh_cliff + 1/2mv_i² = 1/2mv_f²

So if both of the rocks have the same velocity and mass and they both experience the same gravitational pull. They will land at the same time as they have the same energy?

c. Justify using a kinematics argument (projectile motion). The diagram below might help your explanation.

I am still struggling with this one though now

 

[ja!mee]

Hey tiny-tim... It does say in part b of the question that the would indeed hit at the same speed...

 

[tiny-tim]

So if both of the rocks have the same velocity and mass and they both experience the same gravitational pull. They will land at the same time as they have the same energy?

how can they take the same time? look at the diagram (and at part b of the question)

c. Justify using a kinematics argument (projectile motion). The diagram below might help your explanation.

try reflecting that short part of the diagram

 

[ja!mee]

Sorry that was a typo... I fixed it ... they land with the same final velocity.

 

[ja!mee]

sorry does anyone else have any ideas... the last few replies have been cryptic and short