Catching or deflecting an incoming ball for faster velocity?

In summary, the conversation revolves around the question of whether a person on a skateboard should catch or deflect a ball thrown to them in order to achieve the greatest velocity. There is a debate between using the conservation of momentum to calculate the change in momentum or using the concept of force and acceleration to argue for deflection. Ultimately, it is suggested that the lack of details in the question allows for a range of possibilities, but it is believed that deflection has the potential to give a greater velocity due to the freedom in the amount of force that can be exerted.
  • #1
hawainpanda
3
0

Homework Statement


This is a conceptual question:
A ball is thrown to a person (at rest) on a skateboard. Should the person catch or deflect the ball to achieve the greatest velocity.


Homework Equations





The Attempt at a Solution


I thought it would be catching the ball, catching the ball means the force acting on the person for a longer duration of time and therefore larger impulse and larger change in momementum which means larger final velocity.



Thanks!
 
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  • #2
probably better to think of this in conservation of momentum

[itex]m_{s}v_{fs}+m_{b}v_{fb} = m_{s}v_{is}+m_{b}v_{ib}[/itex]

where s = skateboard, b = ball, i = initial, f = final

In each case try to imagine what would happen to the formula
 
  • #3
I already did, using the conservation of momentum I'm right, but my instructor tells me other wise...funny thing is that http://www.sfu.ca/phys/120/PracticeMidterm2.pdf this says I'm correct, question 10.
 
  • #4
in that practice midterm you want to minimize the velocity and catching the ball does that. so you DONT want to catch the ball.

when you deflect the ball you exert a force on it to push it away, and it pushes you by Newton's 3rd Law so you speed up faster than if you just took the entire momentum of the ball.

I think that's how the problem meant to be, maybe wrong wording tho ><
 
  • #5
I think that answer key is wrong...
edit: ok the wording of the practice and your problem is opposite. on the practice exam you want to go slower and on your problem you want to go faster...

Case 1:
[itex](m_b+m_s)v_f=m_bv_{ib}[/itex]

Case 2:
[itex]m_b(-v_{fb})+m_sv_{sf} = m_bv_{ib}[/itex]
[itex]m_sv_{fs}=m_b(v_{fb}+v_{ib})[/itex]
 
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  • #6
you're right, the midterm is the opposite, but I still think I'm right

I did a proof with the conservation of momentum and tried different values and they always proved that catching would create a larger delta momentum
 
  • #7
probably not plugging in a negative velocity when it shoots back the opposite direction
 
  • #8
I'm quite ignorant of all the intricacies and complexities of this topic so, I'm not even sure if my thoughts have any merit here...I'm looking at the question's counterpart found at the link you provided...Some relatively specific statements are made. The ball is "heavy", it goes back to the source, and does so with the same speed at which it came..."Heavy" just hints at its large inertia, and large force required to deflect it (it's multiple choice). Mathematically: If ball is caught, mu=(M+m)v...and v=mu/M+m...right? If ball is deflected...MA=ma, and A=ma/M but a=(v-u)/t = -2u/t...... So A= (-2um)/Mt...but A=(v-0)/t, so v= -2um/M...[Note that Uppercase letters are values for the boy, and lowewrcase for the ball.] Does this make sense? Does it not show that the value for deflection is greater?
 
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  • #9
Once you've caught the ball, its momentum is no longer "acting on you". Your change in momentum is the opposite of the balls change in momentum (so that momentum is conserved). If the ball coming at you has momentum p and you catch it (so it now has momentum 0 relative to you) how much has its momentum changed? If the ball coming at you has momentum p and you deflect it back (so it now has momentum -p) how much has its momentum changed?
 
  • #10
Of course, your question does not tell us that the ball has an equal but opposite velocity after reflection...But, I still believe deflection HAS THE POTENTIAL to give you a larger velocity...I don't know all the scientific fluff involved...but, logically speaking, the lack of details gives you an amazing amount of freedom. The fact is, it is POSSIBLE to deflect the ball with as great a force as you please (of even impractical, unlikely, and purely theoretical magnitudes). With deflection, the force with which the boy is propelled, and thus his acceleration is dependant on the force that he exerts, and lies within an almost infinite range. The acceleration he gains if he catches the ball is constant, while that which he COULD gain by deflection and its resultant is much greater. This may not be the ideal answer, but am I wrong?
 
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1. How does catching or deflecting an incoming ball increase its velocity?

Catching or deflecting an incoming ball can increase its velocity through the principle of conservation of momentum. When the ball collides with a surface (such as a hand or a racket), the momentum of the ball is transferred to the surface. If the surface is able to move, it can transfer this momentum back to the ball, resulting in an increase in velocity.

2. Is it more effective to catch or deflect an incoming ball for faster velocity?

The effectiveness of catching or deflecting an incoming ball for increasing its velocity depends on various factors such as the material and surface of the ball, the angle and speed of the incoming ball, and the skill and technique of the person catching or deflecting it. In general, catching may be more effective for softer and slower balls, while deflecting may be more effective for harder and faster balls.

3. Can the angle at which the ball is caught or deflected affect its velocity?

Yes, the angle at which the ball is caught or deflected can greatly affect its velocity. When the ball is caught or deflected at an angle, the momentum transfer may not be direct, resulting in a change in the direction and speed of the ball. By adjusting the angle, it is possible to redirect the momentum transfer in a more efficient way, resulting in a faster velocity.

4. How can one train to catch or deflect an incoming ball for faster velocity?

Training to catch or deflect an incoming ball for faster velocity involves developing hand-eye coordination, reaction time, and technique. This can be achieved through various drills and exercises that involve catching or deflecting different types of balls at different speeds and angles. Additionally, practicing with a partner or coach can also help improve the skills needed for faster velocity.

5. Are there any safety precautions to consider when catching or deflecting an incoming ball for faster velocity?

Yes, it is important to consider safety precautions when catching or deflecting an incoming ball for faster velocity. This includes using appropriate safety gear, such as gloves or padding, to protect the hands and body from impact. It is also important to be aware of the surroundings and avoid catching or deflecting the ball in a way that may cause injury to oneself or others.

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