KE of a Dropped Bomb: EK Physics

[shaggybill]

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In EK Physics In-Class Exam: Question 61:

If a WWI pilot drops a 2kg bomb from an altitude of 300m, which of these would result in the greatest KE of the bomb just before it hit the ground?

C. The pilot releases the bomb while flying straight down at a velocity of 20m/s.

D. The pilot releases the bomb while flying horizontally at a velocity of 25m/s.


They give the answer as D. I thought it would be C since the bomb has an initial vertical velocity of 20m/s, giving it a higher velocity upon impact, thus a higher KE. Where is my thinking going wrong?

 

[burningheat]

total energy on impact will be mgh + 1/2mv^2 assuming no air resistance, all potential will be converted to kinetic, since hieght is same only take into account KE

 

[shaggybill]

Great! Thanks for your help.

 

[inaccensa]

Great! Thanks for your help.

can u explain that solution plzz

Wouldn't the initial velocity of the bomb be zero? Although the pilot is travelling at 25m/s, the velocity of the bomb at the instant it's dropped won't be zero?

 

[Charles_Carmichael]

Hmmm...

KEi + PEi = KEf + PEf
1/2mv^2 + mgh = KEf + mgh
1/2(2)(20)^2 + (2)(10)(300) = KEf + 0

or

0 + (2)(10)(300) = KEf + 0

Am I missing something here? It seems like C would be the correct answer since both the initial kinetic and potential energies would convert into the final kinetic energy.

 

[shaggybill]

Am I missing something here? It seems like C would be the correct answer since both the initial kinetic and potential energies would convert into the final kinetic energy.

Hmm...interesting point. The bomb is dropped at 300m in both cases, so potential energy is the same, but in (C) the bomb has a higher initial vertical velocity than in (D). Is that what you are saying?

Isn't it only the vertical velocity that we are concerned about here for the KE right before it hits the ground? Does horizontal velocity play a role? Doesn't seem like it.

 

[shaggybill]

Here is the answer in its entirety.

D is correct. Energy is a scalar and is conserved. The total initial energy will equal the final energy in every case. Also, in every case gravitational potential energy will be completely converted to kinetic energy. Since energy is a scalar, the direction of the plane does not affect its initial energy. (Notice that in question 59 we were not concerned with the direction in which the plane was flying.) The initial potential energy is the same in each case. Thus the initial energy and the final energy are greatest where the initial velocity is greatest.

 

[Charles_Carmichael]

Here is the answer in its entirety.

D is correct. Energy is a scalar and is conserved. The total initial energy will equal the final energy in every case. Also, in every case gravitational potential energy will be completely converted to kinetic energy. Since energy is a scalar, the direction of the plane does not affect its initial energy. (Notice that in question 59 we were not concerned with the direction in which the plane was flying.) The initial potential energy is the same in each case. Thus the initial energy and the final energy are greatest where the initial velocity is greatest.

Hmmm...the way I'm thinking, while the initial potential energy is the same for both scenarios, there's also an initial kinetic energy for answer C. I'm thinking of like a slide; when you're sliding down and reached the middle of the slide, you have both kinetic and potential energy that add up to the initial total energy (ie. the PE). And when you reach the bottom of the slide, the intial PE has been fully converted to KE. However, if you start off on the slide in the middle rather than the top, you only have potential energy and not initial kinetic energy and your total energy is smaller in magnitude (since the total energy initially is just the PE and the height is smaller in the second case compared to the first).

Do you see what I'm saying? I feel like, for choice C, the total energy that gets converted to KEf is greater than that in choice D. Like the bomb in choice C started falling from a greater height and we are concerned with it once it reaches 300m above ground.

I don't know. Now I'm confused as well.

 

[loveoforganic]

It's just (1/2)mv^2 + mgh.

Higher initial velocity, same height, higher final kinetic energy. The only cases this could not be true is if the initial velocity was in a direction that had a component opposite in direction to that of the force of gravity.

 

[zmatrix]

Hmmm...the way I'm thinking, while the initial potential energy is the same for both scenarios, there's also an initial kinetic energy for answer C. I'm thinking of like a slide; when you're sliding down and reached the middle of the slide, you have both kinetic and potential energy that add up to the initial total energy (ie. the PE). And when you reach the bottom of the slide, the intial PE has been fully converted to KE. However, if you start off on the slide in the middle rather than the top, you only have potential energy and not initial kinetic energy and your total energy is smaller in magnitude (since the total energy initially is just the PE and the height is smaller in the second case compared to the first).

Do you see what I'm saying? I feel like, for choice C, the total energy that gets converted to KEf is greater than that in choice D. Like the bomb in choice C started falling from a greater height and we are concerned with it once it reaches 300m above ground.

I don't know. Now I'm confused as well.

I think what you and others aren't considering is the fact that having a 20m/s downward velocity also reduces the amount of time it takes to hit the ground (which would also reduce the amount of time it spends accelerating).

C) Vi = 20 down, Vf = 80 down, t = 6 sec, KE = 1/2m(80)^2 = 1/2m(6400)
D) Vi = 0 down, 25 horiz., Vf = 10*sqrt(60) down, 25 horiz., t = sqrt(60), KE = 1/2m([10*sqrt(60)]^2 + 25^2) = 1/2m(6625)

Note that if the horizontal velocity in D had been 20, then we would end up with the same KE as in C - 1/2m(6400)

 

[premed101]

The trap you're falling into is not considering vector addition for initial kinetic energy. If you do the vector addition for initial velocity of answers c and d, you'll find d to have a greater resultant initial velocity.
Here's the tricky part: Because direction doesn't matter, you actually need the resultant velocity as going left or right has absolutely no meaning!

 

[ChemEngSoonMD]

In EK Physics In-Class Exam: Question 61:

If a WWI pilot drops a 2kg bomb from an altitude of 300m, which of these would result in the greatest KE of the bomb just before it hit the ground?

C. The pilot releases the bomb while flying straight down at a velocity of 20m/s.

D. The pilot releases the bomb while flying horizontally at a velocity of 25m/s.


They give the answer as D. I thought it would be C since the bomb has an initial vertical velocity of 20m/s, giving it a higher velocity upon impact, thus a higher KE. Where is my thinking going wrong?

Here is a simpler question. What hurts more, you jumping into a stop sign from a stand still or you jumping out of a car going 60mph into a stop sign? If you said the later, ding ding.