Problem with tether balls - How high should I release the ball

In summary, the question is asking for the release height of a 1 kg tether ball suspended from a string .8 m long, so that it can swing around a circle with a radius of .3 m. The ball must have enough kinetic energy at its lowest point (.8 m below point X) to still have some left when it reaches its highest point (.3 m above point Y). This minimum amount of kinetic energy is needed to keep the string taut. Releasing the ball at a height of .3 m above point Y will not provide enough speed.
  • #1
raferalston
2
0
hi, I am a grade 12 student and am stuck on this question. could somebody help me solve it or solve it for me.
the question is:
A 1 kg tether ball is suspended by a string .8 m long from a nail a point X, .5 m vertically above a horizontal rob at Y. when the ball is released from Z, it swings down and the string catches on Y. how high above Y must the tether ball be released so that it will swing completely around a circle of a radius .3 m about point Y.
 
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  • #2
At its lowest point, .8 m below X, the ball must have enough kinetic energy that, after it has "caught" on y and swings to its highest point .3m above y (and so .6 m above its lowest point- .2 m below X, it still has some kinetic energy left to "get over the top".
 
  • #3
HallsofIvy said:
At its lowest point, .8 m below X, the ball must have enough kinetic energy that, after it has "caught" on y and swings to its highest point .3m above y (and so .6 m above its lowest point- .2 m below X, it still has some kinetic energy left to "get over the top".
Careful... the amount of KE that must be left at the top is non-zero: there is a mimimum amount needed to keep the string taut. (Hint: releasing the ball 0.3m above Y will not give it enough speed.)
 

1. What is the optimal height to release a tether ball?

The optimal height to release a tether ball depends on various factors such as the player's height, arm length, and skill level. Generally, it is recommended to release the ball at a height that allows it to swing freely and hit the pole at a downward angle.

2. How does the height of release affect the game?

The height of release can greatly impact the game of tether ball. A higher release can result in a stronger hit and more momentum, making it harder for the opposing player to return the ball. However, releasing the ball too high can also lead to it swinging out of reach or getting caught in the wind.

3. Is there a specific height that is considered too high to release the ball?

There is no specific height that is considered too high to release the ball. It ultimately depends on the player's ability and comfort level. However, releasing the ball too high may make it difficult to control and could result in a loss of points.

4. What happens if I release the ball at a low height?

Releasing the ball at a low height can make it easier for the opposing player to return the ball and can also result in a weaker hit. It is important to find a balance between releasing the ball too high and too low in order to have a successful game.

5. How can I determine the best height for me to release the ball?

The best way to determine the ideal height to release the ball is through practice and experimentation. Start by releasing the ball at different heights and observe how it affects the game. Adjust accordingly until you find the height that works best for you.

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