Energy and Velocity question.

[Postictal Raiden]

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I know that for an object dropped from an airplane the energy it has the moment before hitting the ground is higher that of a similar object initially at rest dropped from the same height (KEi + PEi = KEf + PEf). Does that also mean that the object dropped from the airplane has a greater final velocity?

 

[regeneration]

The object dropped from the airplane does indeed have greater energy. The velocity in the y direction will be the same for both (only force is gravity), but the object dropped from the airplane will have velocity in the x direction as well. Thus, the SPEED (the magnitude of velocity) will be greater for the object dropped from the airplane.

 

[Postictal Raiden]

The object dropped from the airplane does indeed have greater energy. The velocity in the y direction will be the same for both (only force is gravity), but the object dropped from the airplane will have velocity in the x direction as well. Thus, the SPEED (the magnitude of velocity) will be greater for the object dropped from the airplane.

That makes sense, but why this is not the case in scenarios where objects are being thrown off a cliff with some initial horizontal velocity?

 

[milski]

That makes sense, but why this is not the case in scenarios where objects are being thrown off a cliff with some initial horizontal velocity?

Same horizontal velocity as what? If the object is thrown from a cliff, exactly horizontally, and the horizontal velocity is the same as the airplane's velocity and the airplane is at the same altitude as the cliff, it is the same. It will even be the same if the object is thrown at some angle with the horizon but the magnitude of its velocity is the same as the magnitude of the horizontal speed that we had in the previous case.

The situation may be different if the object is thrown at some angle to the horizon and only its horizontal component of the velocity is the same as before. That implies that there is also a non-zero vertical component, which makes the magnitude of the velocity sort(vx^2+vy^2) which is larger than the previous magnitude, vx^2.

If that's too muddy, I can give you an example with some numbers.

 

[justhanging]

That makes sense, but why this is not the case in scenarios where objects are being thrown off a cliff with some initial horizontal velocity?

What's your reason for it not being the same?

 

[Postictal Raiden]

Sorry, about the confusion.

I understand that the object with the initial horizontal velocity (the one being dropped from an airplane) will have a larger magnitude of energy the moment it contacts the ground than an object being dropped from rest. I was wondering if this difference in energy would translate into a difference in the final velocity of each object, so that the one thrown from the airplane would have a greater velocity.

In his/her response, regeneration explained that the object that was thrown from the airplane will eventually have greater magnitude of velocity before hitting the ground. This response made sense at the beginning, but then it made me wonder, would this also apply for any object with an initial horizontal velocity? For example, if a rock being kicked horizontally off a cliff, will it have a greater velocity before hitting the ground than another rock being simply dropped?

 

[milski]

Sorry, about the confusion.

I understand that the object with the initial horizontal velocity (the one being dropped from an airplane) will have a larger magnitude of energy the moment it contacts the ground than an object being dropped from rest. I was wondering if this difference in energy would translate into a difference in the final velocity of each object, so that the one thrown from the airplane would have a greater velocity.

In his/her response, regeneration explained that the object that was thrown from the airplane will eventually have greater magnitude of velocity before hitting the ground. This response made sense at the beginning, but then it made me wonder, would this also apply for any object with an initial horizontal velocity? For example, if a rock being kicked horizontally off a cliff, will it have a greater velocity before hitting the ground than another rock being simply dropped?

Yes, it will apply in that case too. If the initial velocity is the same, so will be the final velocity (under the same conditions).

Also, be careful with the terminology there - you cannot really say that one velocity is larger than other. Only the magnitudes of the velocities, speeds, can be compared in that way.

 

[Shjanzey]

Technically the Energy is the SAME in both instances.

The difference being that the object at ground level has a higher KINETIC energy, whereas the object yet to be dropped has a higher POTENTIAL energy.

Kinetic energy is defined as 1/2mv^2 and Potential energy is defined as mgh. If you know any of these quantities you can set them equal to each other and solve. So basically as Potential Energy is converted to Kinetic Energy you will see an increase in velocity.

As far as the horizontal velocity, this will be constant throughout the entire time in the air. When you do kinematics, you have to separate the x motion from the y motion.

 

[Meredith92]

Just to clarify, youre asking about the final "resultant" velocity? (the vector sum? In that case it definitely makes sense that anything with an x component (from a plane or kicked off w a horizontal velocity) would have a greater net/ resultant velocity ( thinking about it like the hypotenuse of a triangle is always greater than the two sides).

 

[Postictal Raiden]

Technically the Energy is the SAME in both instances.

The difference being that the object at ground level has a higher KINETIC energy, whereas the object yet to be dropped has a higher POTENTIAL energy.

Kinetic energy is defined as 1/2mv^2 and Potential energy is defined as mgh. If you know any of these quantities you can set them equal to each other and solve. So basically as Potential Energy is converted to Kinetic Energy you will see an increase in velocity.

As far as the horizontal velocity, this will be constant throughout the entire time in the air. When you do kinematics, you have to separate the x motion from the y motion.

I thought energy was conserved. That's why the energy of the object thrown from the airplane is greater than that of the one being dropped from rest. The object thrown from the airplane has the same initial PE as the one being dropped from rest PLUS an initial KE, since it had an initial velocity (the velocity of the plane).

Ignoring air resistance, the airplane object should have a higher magnitude of energy before hitting the ground. The energy will be entirely in form of KE and it will have the same magnitude as its initial PE and KE.

Since airplane object has a greater KE before hitting the ground, it must also has a greater magnitude of velocity too (KE = 1/2 m v^2).

It actually makes since that the airplane object has a greater velocity because it travels a greater distance in the same time as the one being dropped from rest.

 

[Postictal Raiden]

Just to clarify, youre asking about the final "resultant" velocity? (the vector sum? In that case it definitely makes sense that anything with an x component (from a plane or kicked off w a horizontal velocity) would have a greater net/ resultant velocity ( thinking about it like the hypotenuse of a triangle is always greater than the two sides).

Yes, I was asking about the SPEED, the magnitude of velocity before hitting the floor.

 

[milski]

I thought energy was conserved. That's why the energy of the object thrown from the airplane is greater than that of the one being dropped from rest. The object thrown from the airplane has the same initial PE as the one being dropped from rest PLUS an initial KE, since it had an initial velocity (the velocity of the plane).

Ignoring air resistance, the airplane object should have a higher magnitude of energy before hitting the ground. The energy will be entirely in form of KE and it will have the same magnitude as its initial PE and KE.

Since airplane object has a greater KE before hitting the ground, it must also has a greater magnitude of velocity too (KE = 1/2 m v^2).

It actually makes since that the airplane object has a greater velocity because it travels a greater distance in the same time as the one being dropped from rest.

All of this is correct! 👍