Does Air Resistance Cause a Ball to Take Longer Falling Down Than Rising Up?

[yoyo16]

Homework Statement

If a ball is thrown upwards and lands in the same spot, would it take longer to reach max height or drop back down from the max height? Also use air resistance.

Homework Equations

The Attempt at a Solution

I believe that it would take longer for the object to fall back down. I think it is because that when throwing a ball upwards, gravity would be positive and for ex. if a ball was thrown with acceleration of 2m/s^2, you would add two to 9.8 which would help the ball go up faster while when falling down, the ball air resistance would be in the opposite direction causing the ball to fall back slowly. I'm not sure how to explain my answer properly. This is what I understand so far, if I'm not correct can someone please explain this too me.

Thanks,

 

[paisiello2]

You are not correct.

First of all let's assume air resistance is a function of velocity and it creates a drag force in the opposite direction of motion.

Second, you can't throw anything with an acceleration once it leaves your hand. You can only accelerate it over the time your hand can continue to exert a force on it. Once it leaves your hand it will only have an initial velocity.

Do you know the kinematic equations of motion?

 

[yoyo16]

Yes. How would you use that when explaining the answer for this question?

 

[NascentOxygen]

Yes. How would you use that when explaining the answer for this question?

I doubt that you will be able to account for your answer mathematically without resorting to the use of caculus. (By the way, air resistance always acts to oppose the motion.)

But perhaps you should ponder an extreme example. (Hint: terminal velocity)

 

[HalfLostAndSearching]

I can provide a more detailed explanation for your question about air resistance and the time it takes for an object to reach maximum height and fall back down.

When an object, such as a ball, is thrown upwards, it experiences both gravitational force and air resistance. The force of gravity pulls the ball towards the Earth, while air resistance acts in the opposite direction, slowing down the ball's motion.

As the ball is thrown upwards, it gains kinetic energy from the initial force applied. This kinetic energy is then converted into potential energy as the ball reaches its maximum height. At this point, the ball's velocity is zero and it begins to fall back down.

Now, let's consider the effects of air resistance on the ball's motion. As the ball falls, it experiences a drag force from the air resistance, which increases as the ball's velocity increases. This drag force acts in the opposite direction of the ball's motion, slowing it down. This means that the ball takes longer to fall back down to its starting point compared to the time it took to reach maximum height.

In summary, the presence of air resistance affects the time it takes for an object to reach maximum height and fall back down. The ball takes longer to fall back down due to the opposing force of air resistance acting on it. I hope this explanation helps to clarify your understanding of the concept.