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Question 1189951: Hello, these are physics problems. Help please
1. A 0.22 kg red striped pool ball is moving at 3.0 m/s North and it collides with a white cue ball that is 0.25 kg and it is moving at 1.0 m/s South. After the collision, the red striped ball continues at 2.5 m/s North. What is the velocity of the white cue ball?
2. Two skaters are skating towards each other. The 75.0 kg man is moving at 2.0 m/s to the right, and he picks up the 40.0 kg woman skater who is moving at - 1.5 m/s to the left. What speed and direction do they move off together (assuming no friction on the ice)?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
A 0.22 kg red striped pool ball is moving at 3.0 m/s North and it collides with a white cue ball that is 0.25 kg and it is moving at 1.0 m/s South. After the collision, the red striped ball continues at 2.5 m/s North. What is the velocity of the white cue ball?
Law of conservation of momentum.
Momentum before collision = momentum after collision
Mass of ball I m1
Initial velocity u1
Mass of ball II m2
initial velocity v2
initial momentum = m1u1+m2u2
After collision the momentum will be
m1v1 + m2v2
v1 velocity of ball I after collision
v2 velocity of ball II after collision x
0.22 * 3 + 0.25 * 1 = 0.22*2.5 + 0.25 *x
0.66 + 0.25 = 0.550 +0.25x
0.91 -0.55 = 0.25x
0.36= 0.25x
x = 1.44 m/s ( Ball II)
Problem II similar
m1u1+m2u2 = (m1+m2) *v
They have common velocity after they meet.
2. Two skaters are skating towards each other. The 75.0 kg man is moving at 2.0 m/s to the right, and he picks up the 40.0 kg woman skater who is moving at - 1.5 m/s to the left. What speed and direction do they move off together (assuming no friction on the ice)?
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
1. A 0.22 kg red striped pool ball is moving at 3.0 m/s North and it collides with a white cue ball
that is 0.25 kg and it is moving at 1.0 m/s South. After the collision, the red striped ball continues
at 2.5 m/s North. What is the velocity of the white cue ball?
2. Two skaters are skating towards each other. The 75.0 kg man is moving at 2.0 m/s to the right,
and he picks up the 40.0 kg woman skater who is moving at - 1.5 m/s to the left.
What speed and direction do they move off together (assuming no friction on the ice)?
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The solution by @mananth to problem 1 is ABSOLUTELY WRONG. So, I came to bring correct calculations.
Next, the problem itself is posed INCORRECTLY, as I will explain it in my post-solution note.
Problem 1
Since two balls move in opposite directions, vectors along North axis contribute with the " + " sign,
while vectors along South axis contribute with the " - " sign ".
The momentum of the red ball before collision is  = 0.22*3 = 0.66 (kg*m)/s.
The momentum of the white ball before collision is  = -0.25*1 = -0.25 (kg*m)/s.
The momentum of the red ball after collision is  = 0.22*2.5 = 0.55 (kg*m)/s.
The momentum conservation law states that the total moment after collision is the same as before collision
+ = + 
or
0.66 - 0.25 = 0.55 + , in (kg*m)/s.
From this equation, you find the momentum of the white ball after collision
= 0.66 - 0.25 - 0.55 = -0.14 (kg*m)/s.
As the last step, you find the velocity of the white ball after collision by dividing its momentum by its mass
velocity of the white ball after collision =  = -0.056 m/s.
The sign "-" tells that white ball moves south after collision.
At this point, the formal calculations are completed.
But look what we get.
The red ball initially moved North and continues moving North after collision.
The white ball initially moved South and continues moving South after collision.
It means, physically, then the balls " penetrated " through each other,
which physically may not happen with real balls (no one physical experiment, so far, showed similar phenomenon).
Therefore, I think that the problem is posed physically INCORRECTLY.
No one real physical experiment may produce such a combination of input values as presented in your post.
The problem as posed, with provided input data is a FAKE.
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The solution by @mananth is wrong, since he uses incorrect expressions for the momentum,
placing incorrect signs there.
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