Time taken to reach max/min height

In summary, air resistance affects the motion of a ball thrown vertically by slowing it down throughout its entire flight. This is because air resistance is constant and is present both on the way up and down. However, the acceleration on the way up is greater due to the initial throw, causing the time to reach maximum height to be shorter compared to the time taken to return to the starting point. This is because the downward acceleration is less than the upward acceleration due to air resistance.
  • #1
wadevala
4
0
y for all real vertical throw, the time taken to reach max height must b shorter than time taken to return to starting point?

the answer given to me by a teacher is that in the upward motion, the max spd and deceleration are more so the time to travel the dist is shorter, and in the downward motion the max spd and acceleration are lower so the time taken to travel this dist is longer.

however i dun quite understand this explanation, can someone explain it more clearly to me..thx
 
Physics news on Phys.org
  • #2
Hi wadevala! :smile:

If we ignore air resistance, your teacher is talking rubbish. :frown:

The path is is determined by a quadratic equation … it would be a parabola if it wasn't completely vertical … the speed at each point on the way up is the same as on the way down … if you took a film of it, and forgot which way round the film was, nobody could tell whether you were running the film forwards or backwards. :smile:

With air resistance, the ball is losing energy, so basically it'll go slower than it should on the way down, which means that the time to go down will be longer, but not for the reason he/she gave.
 
  • #3
wadevala said:
y for all real vertical throw, the time taken to reach max height must b shorter than time taken to return to starting point?

the answer given to me by a teacher is that in the upward motion, the max spd and deceleration are more so the time to travel the dist is shorter, and in the downward motion the max spd and acceleration are lower so the time taken to travel this dist is longer.

however i dun quite understand this explanation, can someone explain it more clearly to me..thx

tiny tim is correct, and the fact that you are having a problem in understanding your teacher's explanation tells me that you are thinking of this correctly. So well done!

Zz.
 
  • #4
Why is air resistance different in the two paths up and down? Shouldn't they be same since the velocities are just the same in both the paths?
 
  • #5
manjuvenamma said:
Why is air resistance different in the two paths up and down? Shouldn't they be same since the velocities are just the same in both the paths?

Hi manjuvenamma! :smile:

(you mean "the velocities are equal and opposite" or "the speeds are the same")

You're right that air resistance is the same up as it is down, for the same speed.

But the speeds aren't the same (at the same heights), because the (downward) acceleration is greater on the way up.

If air resistance is mAdx/dt, the the downward acceleration is g + Adx/dt; on the way up, that's more than g, and on the way down it's less than g; the greater the speed, the greater the difference. :smile:
 
  • #6
manjuvenamma said:
Why is air resistance different in the two paths up and down? Shouldn't they be same since the velocities are just the same in both the paths?
Yes, the air resistance is the same on the way up as it is on the way down. However, on the way up, the ball has just been thrown. On the way down, the ball has been in flight for some time. As Tiny Tim said, this resistance will change at different speeds, but it will continue to be present while the ball is in flight. So, if you imagine throwing the ball in a straight and level line, you know that it will continually slowdown due to air resistance throughout its entire flight.

The same is true for a vertical throw. Throw the ball straight up and down in a vacuum, and it will take the same amount of time to reach its maximum height as it does to return to the point from which it was thrown. But in an atmosphere, wind resistance will continue slowing the ball's progress all the way through its flight.
 
  • #7
Hi Tiny Tim,

"But the speeds aren't the same (at the same heights), because the (downward) acceleration is greater on the way up."

The speeds should be the same at the same heights, and acceleration is also constant throughout the flight, that is what we assume and use in all our calculations. Of course, this is not considering air resistance. Now if you include air resistance, that will slow down the movement, but why do you think it will affect differently in the two paths up and down?

When so many of you are saying it is the way, I agree that it is most probably is the way, but I am not able to understand the cause or explanation you are giving.
 
  • #8
Hi manjuvenamma! :smile:
manjuvenamma said:
The speeds should be the same at the same heights, and acceleration is also constant throughout the flight, that is what we assume and use in all our calculations. Of course, this is not considering air resistance.

That's right! :smile:
Now if you include air resistance, that will slow down the movement, but why do you think it will affect differently in the two paths up and down?

Because it changes the acceleration:
tiny-tim said:
If air resistance is mAdx/dt, the the downward acceleration is g + Adx/dt; on the way up, that's more than g, and on the way down it's less than g; the greater the speed, the greater the difference. :smile:

Have you done any problems in which there are two weights M and m connected by a rope which goes round a pulley?

Each weight moves with an acceleration of g times ±(M - m)/(M + m) … until the rope breaks, or one weight hits the ground!

Similarly, air resistance means that the acceleration is no longer g … and it's different on the way down from the way up! :smile:
 
  • #9
Hi Tiny Tim,

I am a beginner in Physics. I found joy in solving kinematics problems and predicting horizontal ranges, max heights etc etc. where throughout I assumed g is constant. Now also I think we should say g is constant but now we have to take into account another factor i.e air resistance which we all know is real and exists.

How that affects the velocity of the stone is the questions. I believe g is independent of the air resistance and does not get affected.

Now, I know nothing about air resistance beyond my guess that that is some kind of friction and slows down the relative motion in both the ways. You seem to be saying some thing different with an equation.

I have not yet done anything with pulleys.

I will try to understand explanation after I finish with your pulley analogy. I win my bread with software development, so it takes a bit of time to absorb your explanation. Thanks for your time and patience.
 
  • #10
Hi manjuvenamma! :smile:
manjuvenamma said:
Now also I think we should say g is constant but now we have to take into account another factor i.e air resistance which we all know is real and exists.

How that affects the velocity of the stone is the questions. I believe g is independent of the air resistance and does not get affected..

Yes that's right, of course … g itself is not affected. :smile:

And g is independent of speed, while air resistance obviously isn't.

So when you're making calculations (as opposed to just a rough description, as here), you do have to treat them separately! :smile:
Now, I know nothing about air resistance beyond my guess that that is some kind of friction and slows down the relative motion in both the ways. You seem to be saying some thing different with an equation.

I have not yet done anything with pulleys.

Actually, my equation is the usual friction equation … the force of friction is a constant (usually written µ, pronounced "mu") times the velocity (and directly opposite to the velocity). So the extra acceleration from friction is -µdx/dt. :smile:

Air resistance is slightly different at low speeds, basically because the air gets dragged along with the object, and very different at higher speeds (think of terminal velocity, and turbulence round wings).

For pulleys, I suggest you do a forum search for "pulley", and try some examples! :smile:
 
  • #11
let's just go like this: gravity: 10 m/s^2, friction: (assume constant) 2 m/s^2

so when the ball was moving upwards, the acceleration was: 12 m/s^2 slowing it down
when the ball was moving downwards, the acceleration was 8 m/s^2 speeding it up downwards

and because the distances traveled on both ways are the same, call it H, from the simple equation H=(a*t^2)/2 we can see that the time taken would be longer for the downfall, right?

i knew that this approximation is the silliest thing ever mentioned in this thread, but i hope it helps to visualize the problem
 

1. What factors affect the time taken to reach maximum/minimum height?

The time taken to reach maximum/minimum height is affected by several factors, such as the initial velocity, acceleration due to gravity, air resistance, and the height of the object. These factors can either increase or decrease the time taken to reach maximum/minimum height.

2. How does changing the initial velocity affect the time taken to reach maximum/minimum height?

The initial velocity of an object has a direct impact on the time taken to reach maximum/minimum height. A higher initial velocity will result in a shorter time taken to reach the peak or lowest point, while a lower initial velocity will result in a longer time taken to reach these points.

3. How does air resistance affect the time taken to reach maximum/minimum height?

Air resistance can significantly affect the time taken to reach maximum/minimum height. Objects with a larger surface area or shape that creates more drag will take longer to reach maximum/minimum height due to the opposing force of air resistance. On the other hand, objects with a smaller surface area or streamlined shape will experience less air resistance and reach maximum/minimum height faster.

4. Does the height of the object affect the time taken to reach maximum/minimum height?

Yes, the height of the object does affect the time taken to reach maximum/minimum height. The higher the starting point of the object, the longer it will take to reach maximum/minimum height due to the increase in potential energy. Similarly, starting from a lower height will result in a shorter time taken to reach maximum/minimum height.

5. How does the acceleration due to gravity affect the time taken to reach maximum/minimum height?

The acceleration due to gravity plays a crucial role in determining the time taken to reach maximum/minimum height. The higher the acceleration due to gravity, the faster the object will accelerate and reach maximum/minimum height in a shorter period. On the other hand, a lower acceleration due to gravity will result in a longer time taken to reach these points.

Similar threads

Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
16
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
986
  • Introductory Physics Homework Help
Replies
15
Views
20K
  • Classical Physics
Replies
30
Views
3K
Replies
5
Views
1K
  • Other Physics Topics
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
5K
  • Introductory Physics Homework Help
Replies
13
Views
2K
Replies
13
Views
2K
Back
Top