Two Balls Thrown from Cliff: Speed of Impact

In summary, two balls are thrown at equal speeds from the top of a cliff of height H, with one ball thrown upward at an angle @ above the horizontal and the other thrown downward at an angle # below the horizontal. It can be shown that both balls will strike the ground with the same speed, which can be found in terms of H and the initial velocity v'. Conservation of something can be used to solve this problem.
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naveed4394
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two balls are thrown with equal speeds from the top of a cliff of height H. one ball is thrown upward at an angle @ above the horizontal. the other ball is thrown downward at an angle # below the horizontal. show that each ball strikes the ground with same speed and find that speed in terms of H and the initial velocity v'.



hope that some one will solve this problem for me . with gratitude
 
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Welcome to PF!

naveed4394 said:
two balls are thrown with equal speeds from the top of a cliff of height H. one ball is thrown upward at an angle @ above the horizontal. the other ball is thrown downward at an angle # below the horizontal. show that each ball strikes the ground with same speed and find that speed in terms of H and the initial velocity v'. some one will solve this problem for me . with gratitude

Hi naveed4394! Welcome to PF! :smile:

Hint: use conservation of … something! :wink:
 

FAQ: Two Balls Thrown from Cliff: Speed of Impact

What is the speed of impact for two balls thrown from a cliff?

The speed of impact for two balls thrown from a cliff depends on various factors, such as the height of the cliff, the initial velocity of the balls, and air resistance. However, in a vacuum with no air resistance, the speed of impact will be the same for both balls and can be calculated using the formula v = √(2gh), where v is the speed of impact, g is the acceleration due to gravity, and h is the height of the cliff.

How does the weight of the balls affect the speed of impact?

The weight of the balls does not affect the speed of impact in a vacuum with no air resistance. This is because in a vacuum, all objects fall at the same rate regardless of their weight, due to the acceleration of gravity being constant. However, in the presence of air resistance, a heavier ball may experience a slightly slower speed of impact due to the additional force of air resistance acting on it.

Can the speed of impact be higher than the initial velocity of the balls?

Yes, the speed of impact can be higher than the initial velocity of the balls. This can happen if the balls are thrown at an angle, causing them to travel a greater horizontal distance before reaching the ground. Therefore, even though the initial velocity may be the same for both balls, the one that travels a greater horizontal distance will have a higher speed of impact.

How does air resistance affect the speed of impact?

Air resistance can significantly impact the speed of impact for objects falling from a cliff. As the balls fall, they will experience a force of air resistance that will act against their motion and slow them down. This means that the speed of impact will be lower than the calculated value in a vacuum, and the heavier ball may experience a greater decrease in speed due to air resistance.

What other factors can affect the speed of impact for two balls thrown from a cliff?

Aside from the height of the cliff, initial velocity, weight, and air resistance, other factors that can affect the speed of impact include the shape and size of the balls, the angle at which they are thrown, and the density of the air. These factors may have a small or negligible impact on the speed of impact, but they should be considered when conducting experiments or making calculations.

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