What is the Correct Calculation for h/H When Ball A Collides with Ball B?

In summary, two balls, A and B, are dropped and thrown respectively, with A starting from a building of height H and B starting from the ground. When they collide at height h, A has twice the speed of B. However, in solving for the collision, the equation shows that A has a speed four times greater than B. This discrepancy is resolved by factoring in the initial velocity and acceleration of B. By solving for H and t in terms of these variables, the equation can then be rewritten to accurately show A having twice the speed of B at the time of collision.
  • #1
Juliusz
13
3

Homework Statement


Ball A is dropped from rest from a building of height H exactly as ball B is thrown up vertically from the ground. When they collide A has twice the speed of B. If the collision occurs at height h, what is h/H?

Homework Equations


L9rtuun.png

(I would type them out put I can't format them properly, sorry)

The Attempt at a Solution


ZH9mqyG.png


I did everything as in the example, but then I got to the part where we compare the speeds. The formula (red arrow) show that at the time of impact, the speed of A is 4 times greater than speed of B. But in the problem, it states that the speed of A is only twice the speed of B. So my understanding is that there should be a 2 instead of a 4. Am I missing something?
 

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  • #2
Juliusz said:
Am I missing something?

The equation is in ##v^2##.
 
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  • #3
Ah, I think I see. So it can be written like this?
GJDOdpq.png
 

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  • #4
Alternate method based on relative velocity of A and B as well as the speed relation when they collide:

Solve simultaneously for H and t (in terms of u - initial velocity of B - and g):

t = H/u ......Eqn 1
2(u-gt) = gt ....Eqn 2

Then h = ut - 0.5 g t^2.
 

Related to What is the Correct Calculation for h/H When Ball A Collides with Ball B?

1. What is basic vertical object collision?

Basic vertical object collision is the concept of two objects colliding with each other in a vertical direction. This can occur in scenarios such as objects falling from a height and hitting the ground, or two objects moving towards each other in a straight vertical path.

2. How is the velocity of the objects involved in vertical collision calculated?

The velocity of the objects can be calculated using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity, and t is the time taken for the collision to occur. This assumes that the objects are only affected by gravity and there are no other external forces at play.

3. What factors can affect the outcome of a vertical object collision?

The main factors that can affect the outcome of a vertical object collision include the mass and velocity of the objects, the coefficient of restitution (a measure of how much energy is lost during the collision), and any external forces acting on the objects such as air resistance or friction.

4. How does the angle of impact affect a vertical object collision?

The angle of impact can significantly alter the outcome of a vertical object collision. If the objects collide at a right angle, the velocity of both objects will change in the opposite direction. However, if the angle of impact is not perpendicular, the final velocities will have both a vertical and horizontal component, resulting in a more complex collision.

5. Is there a difference between elastic and inelastic vertical object collisions?

Yes, there is a significant difference between elastic and inelastic vertical object collisions. In an elastic collision, the two objects bounce off each other with no loss of energy, resulting in a change of direction and speed for both objects. In an inelastic collision, some energy is lost during the collision, resulting in a decrease in the final velocity of the objects.

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