# Question which one travels faster?

#### kashmirekat

Question....which one travels faster?

I had this question on a homework assignment and I was hoping someone could help me understand why I got it wrong.

A ball is thrown down from a building and another ball is thrown up with the same amount of velocity. What is their speed when they hit the street?

a. the one thrown up is travelling faster
b. the one thrown down is travelling faster
c. the speeds are the same
d. cannot be determined

The answer I chose was [a] because it is going to travel up until the velocity reaches zero at which point it will fall a greater distance (therefore gaining more speed on the way down) than that of the ball initally thrown down.

Please correct me if I am wrong and tell why. Thank you and have a nice day!
Christina

• deyaaa

#### jcsd

Gold Member
I'm slightly confused, is the second ball thrown upwards from the top of the building or from ground level?

Anyway assuming that the second ball is thrown from the top of the builing, ignoring terminal velocity, yes it will hit the street faster as (assuming the inital velocity, u = 0) for v, velocity, a accleration and s distance:

v = as

for both of them a = g (accelartion due to gravity)

therefore the larger s (in tis which should be defined as the distance fallen) the large v.

So yes you're correct, the answer you want is a)

#### kashmirekat

Yes, the second ball was thrown from the building.

Thank you! I thought I was correct and I was peeping at other folks' papers and they all chose 'the same speed', and got it right mind you. I find that interesting.

Another question I got wrong was a ball (ball A) is dropped from a building, one second later another ball (ball B) is dropped from the same building. What is the distance between the two balls?

a. remains constant
b. increases
c. decreases
d. cannot be determined

I chose a. remains constant. They are both falling at the same rate, they are going to gain the same acceleration on the way down with only a second difference. Ball A will hit the ground first, but ball B will hit one second later. The answer my instructor gave was 'b. increases'. I just don't understand how the distance could increase when the rate they are falling is the same.

Christina

#### jcsd

Gold Member
Remember the first ball to be thrown will always be travelling at a greater speed compared to the second ball as it would of had more time to accelerate, so the distance between the two is always getting larger.

#### marcus

Gold Member
Dearly Missed
jcsd, as you suggest by mentioning terminal velocity all these problems depend so much on one's assumptions
with my assumptions I seem to get a different answer

I assume air resistance is ignored, the building is like in a vacuum(!)

and that both balls are thrown from the roof (where they have the same potential energy) and given the
same kinetic energy

so they both start out with the same amount of energy

so I think of them as having the same when they hit ground

I was thinking of them as identical balls but it doesnt matter
if one's bigger since its really just energy per unit mass that's the same

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#### Sonty

I think so, too, marcus.

#### russ_watters

Mentor
edit: bah, I misread the problem. I was thinking the ball thrown up was being thrown up from the street. Yeah, they both land at the same speed. [hangs head in shame]

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#### Integral

Staff Emeritus
Gold Member
Remember that, neglecting air resistance, a ball thrown up has the same speed it had on the way up at each height on the way down. Thus when it returns to the top of the building it will have the same velocity as the other ball, therefore it hits the ground with the same velocity.

#### marcus

Gold Member
Dearly Missed
Christina,

it is very pleasant to have a physics problem like these in the morning, so thanks for contributing. Bring in some more like these if you have them!

Advice: if you dont understand the replies keep asking questions.

About the first question: Sonty (a romanian student) says the answer is C-----they hit with the same speed.

If you dont see why, ask him! It would be good practice for him to explain.

About the second question: JCSD says the answer is B-----the distance caused by a one-second delay increases with speed. If you dont understand ask him to explain further.

There is also a Homework Help section of this board. This is a great board. We also have great crazies. You should visit us daily. post script: oops also Integral the local mentor Honcho has replied----you are getting red carpet treatment!

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#### HallsofIvy

The answer I chose was [a] because it is going to travel up until the velocity reaches zero at which point it will fall a greater distance (therefore gaining more speed on the way down) than that of the ball initally thrown down.
The reason this NOT correct is that, while the second ball is "gaining more speed on the way down", it starts downward (from its highest point)at 0 velocity while the first ball started downward with an initial velocity.
If the problem had said the first ball were DROPPED while the second ball was thrown upward, you would be correct.

The really important question is "what is the velocity of the second ball when it is again at the original position (on its way down)?"

#### FZ+

The answer is thatt they both land at the same speed, assuming their initial speeds were the same and no air resistance. How?

Use the energy calculation.

Final KE = Initial GPE + Initial KE.

Notice that initial GPE is the same for both balls.

Also notice that KE = 0.5 * mv^2 - and is independent of + or - velocity.

Therefore, the final KE of both is the same, and so both land at the same speed. The time of landing is very different, of course.

#### kashmirekat

I understand the first problem I asked. However, I am still not fully understanding the one with ball a dropped and then ball b dropped one second later. When they hit the ground, ball a will hit first, and then ball b will hit one second later, right? So how could the distance between them increase? Ball A accelerates faster, true because it was dropped first. However, Ball B accelerates at the same velocity (the pull of gravity) as that of A, only a second behind. I know that over a period of time objects falling fall faster. But when ball A increases its acceleration downward at a certain time, ball B also increases its acceleration downward at a later time of one second.

Sorry if this sounds trivial, but I'm just trying to understand. Thank you for all of your help.

Christina

#### FZ+

Well, you know that the objects are undertaking linear acceleration, right?

This means that you have a straight line graph in V against time, and to find the distance, you take the area under that. Correct?

Now you know from the linear acceleration that final velocity = kt, where k is some constant. (I'm not going to use exact values, just given a feel of the quality of behaviour). And that the total distance travelled is equal to A (another constant) * v * t

Hence, we get the idea that the distance travelled is proportional to the square of the time.

Now, the difference in distance between the two is then proportional to (where x is the time delay)...

= B * ( T^2 - (T-x)^2)
= B* (T^2 - T^2 - x^2 + 2*T*x)
= B * 2 * T * x - B * x^2

And T is time, obviously the difference in distances increases.

#### jcsd

Gold Member
Originally posted by Integral
Remember that, neglecting air resistance, a ball thrown up has the same speed it had on the way up at each height on the way down. Thus when it returns to the top of the building it will have the same velocity as the other ball, therefore it hits the ground with the same velocity.
hmmm, you see I considered the first ball to be dropped not thrown, I realize now that I misread the question.

#### Integral

Staff Emeritus
Gold Member
I had to read the question several times and then read some responses before figured out what the question was. Seems to be rather poorly worded.

#### kashmirekat

I fully understand now. Thank you all for your help. Sorry for any poor wording, I didn't have the assignment with me and tried to remember the basis of what the question asked.

Integral the local mentor Honcho has replied----you are getting red carpet treatment!
I feel so special.

You should visit us daily.
I do believe I will do that. You people are very insightful and helpful in answering my questions. I have another homework assignment so I will probably be posting on the homework board for further assistance.

Thanks again for everyone's help. I understand. Nothing tops that. :)

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