How long does a ball take to reappear at a certain point when it is thrown up?

In summary, the physicist observed a ball moving straight upward outside her window for 0.25 seconds, covering a distance of 1.06 meters from the bottom to the top of the window. The questions posed were: how long would it take the ball to reappear and what is the greatest height of the ball above the top of the window? To solve this, the kinematic acceleration equations vf2 = vi2 + 2a\Deltax and x = xi + vit + 1/2 at2 were considered appropriate. The only significant force acting upon the ball is gravity, and any other forces can be considered negligible. Moving the coordinate plane to the bottom of the window, it can be assumed that the ball was launched from
  • #1
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Homework Statement



Sitting in a second-story apartment, a physicist notices a ball moving straight upward just outside her window. The ball is visible for 0.25 s as it moves a distance of 1.06 m from the bottom to the top of the window.

How long does it take the ball to reappear?
What is the greatest height of the ball above the top of the window?

Homework Equations





The Attempt at a Solution

 
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  • #2
What kinematic acceleration equations would you considered appropriate when describing a ball falling down from a two story building? What forces are acting upon the ball as it falls down? What forces would you consider negliglble in this scenario?
 
  • #3
vf2 = vi2 + 2a[tex]\Delta[/tex]x

x = xi + vit + 1/2 at2
 
  • #4
Move your coordinate plane so the x-axis is on the bottom of the window. You can ignore everything that happens below the window, in fact you can pretend that the ball was launched right at the bottom of the window. You know that it took .25s to travel 1.06m so now just find Vo
 

1. How is the time it takes for a ball to reappear calculated?

The time it takes for a ball to reappear at a certain point when it is thrown up is calculated using the formula t = √(2h/g), where t is the time in seconds, h is the height of the throw, and g is the acceleration due to gravity (9.8 m/s²).

2. Does the weight of the ball affect the time it takes to reappear?

No, the weight of the ball does not affect the time it takes for the ball to reappear. The only factors that affect the time are the initial height of the throw and the acceleration due to gravity.

3. Can air resistance slow down the time it takes for the ball to reappear?

Yes, air resistance can slightly slow down the time it takes for the ball to reappear. However, this effect is usually negligible for objects like balls that are thrown at low speeds.

4. Does the angle of the throw affect the time it takes for the ball to reappear?

Yes, the angle of the throw can affect the time it takes for the ball to reappear. If the ball is thrown at an angle, it will follow a curved path and take longer to reappear at the same point compared to a ball thrown straight up.

5. Why does the time it takes for the ball to reappear decrease with increasing initial height?

The time it takes for the ball to reappear decreases with increasing initial height because the ball has more potential energy when thrown from a higher point. This potential energy is converted into kinetic energy as the ball falls, resulting in a faster descent and shorter time to reappear at the same point.

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