What is the height of a ball after being in the air for T/4 seconds?

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In summary, a child tosses a ball directly upward with a total time in the air of T and a maximum height of H. The height of the ball after being in the air for T/4 is 1/4 H, but the exact answer is unknown. Using the equation y=vot +0.5 at², we can solve for t and find the initial velocity, vo. By considering the second half of the motion, we can determine that the ball drops down by H over a time of T/2, and therefore drops down by 1/4 H in T/4. This information can be used to find the correct answer for the ball's height after T/4.
  • #1
robax25
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Homework Statement



A child tosses a ball directly upward. Its total time in the air is T. Its maximum height is H. What is its height after it has been in the air a time T/4? Neglect air resistance.

Homework Equations


y=vot +0.5 at²

The Attempt at a Solution


It is 1/4 H but I don't get exact answer.
 
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  • #2
robax25 said:

Homework Statement



A child tosses a ball directly upward. Its total time in the air is T. Its maximum height is H. What is its height after it has been in the air a time T/4? Neglect air resistance.

Homework Equations


y=vot +0.5 at²

The Attempt at a Solution


It is 1/4 H but I don't get exact answer.

What answer do you get? Please show.

At what time do you think the ball reaches the maximal height H?
 
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  • #3
t/2 second
 
  • #4
robax25 said:
t/2 second

What value are you able to obtain with that information and the equation you posted in section 2 of the template in your first post?
 
  • #5
y=v(t/2)-0,5a(t/2)² when the ball is at maximum height and vo is equal to gt/2
 
  • #6
robax25 said:
y=v(t/2)-0,5a(t/2)² when the ball is at maximum height and vo is equal to gt/2

So, you can find ##t## from the first equation (using ##y = H##, a given input in the problem); then, after finding ##t## you can figure out ##v_0##. Take it from there.

By the way: either use ##g## or ##a##, but not both notations in the same problem, given that they are both supposed to be the same quantity.
 
  • #7
robax25 said:
y=v(t/2)-0,5a(t/2)² when the ball is at maximum height and vo is equal to gt/2

Stay with the definition that ##v_0## is the velocity of the ball when it leaves the child's hand, which is what you want to calculate to find the answer of the original problem (##v_0=f\left(g, T, H\right)##).
 
  • #8
There is no need to find the initial velocity.
robax25 said:
t/2 second
What is t? Why did you add "seconds"?
I guess you mean T/2 - just half of the total air time. That is correct.

Consider the second half of the motion for a moment: How can you describe how far it fell down from the highest point as a function if time?
It drops down by H over a time of T/2. How much does it drop down in half of that time, in T/4? While that is not the final answer to the problem you can transfer that result to get the right answer.
 

1. What is the force that makes the ball go up when thrown?

The force that makes the ball go up when thrown is the initial force of the throw, also known as the launch force. This force is generated by the arm and hand of the thrower pushing the ball upwards with a certain amount of energy.

2. Why does the ball eventually fall back down?

The ball eventually falls back down due to the force of gravity. Gravity is the natural force that pulls objects towards the center of the Earth. As the ball travels upwards, the force of gravity acts on it, slowing it down until it eventually falls back to the ground.

3. How does air resistance affect the trajectory of the ball?

Air resistance, also known as drag, is the force exerted by the air on a moving object. When a ball is thrown upwards, air resistance acts against its motion, slowing it down and affecting its trajectory. This is why objects with a greater surface area, such as a feather, experience more air resistance and fall slower than objects with a smaller surface area, such as a ball.

4. Can the height of the throw affect the ball's trajectory?

Yes, the height of the throw can affect the ball's trajectory. The higher the ball is thrown, the longer it has to travel against the force of gravity. This means it will reach a greater height before falling back down. However, the initial force of the throw will also play a role in the ball's trajectory.

5. Is the force of the throw the only factor that affects the ball's trajectory?

No, there are other factors that can affect the ball's trajectory, such as air resistance, the angle of the throw, and any external forces, such as wind. The force of the throw is the initial force that determines the ball's speed and direction, but these other factors can influence its path as it travels upwards and falls back down.

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