A baseball pitcher litter a baseball at 

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 horizontally in the confident direction to a batter, who hits the round in the contrary direction at
\"*\"
. What is the readjust in momentum of the baseball if the baseball has a mass of 
\"*\"
?


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Explanation:

In stimulate to calculation the adjust in momentum, us must discover the initial and final momentum of the baseball, and also then discover the difference.

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Use the provided velocities and mass to calculation the initial and final values.

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The initial inert is positive since the trouble states that the ball was initially thrown in the hopeful direction. The last momentum is an unfavorable due come the change in direction.

Now we uncover the adjust in momentum:

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Ball A, traveling 

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to the right, collides with sphere B, traveling 
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to the left. If ball A is 4kg and ball B is 6kg, what will be the final velocity and also direction after ~ a perfect inelastic collision?


Explanation:

A perfect inelastic collision is when the two bodies stick together at the end. At the beginning the 2 balls space traveling separately with individual inert values. Using the inert equation

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, we can see that round A has actually a inert of (4kg)(7m/s) to the right and also ball B has a momentum of (6kg)(8m/s) come the left. The last momentum would certainly be the massive of both balls times the final velocity, (4+6)(vf). We deserve to solve for vf through conservation of momentum; the sum of the initial momentum values should equal the last momentum.

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Note: sphere B\"s velocity is an adverse because they are traveling in opposite directions.

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The an unfavorable sign shows the direction in which the 2 balls space traveling. Because the sign is negative and we indicated that travel to the left is negative, the 2 balls have to be traveling 2m/s come the left ~ the perfectly inelastic collision.


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Example inquiry #1 : expertise Momentum and Impulse


Two astronauts, Ann and Bob, command a collision experiment in a weightless, frictionless environment. Initially Ann moves to the right with a inert of 

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, and also Bob is initially at rest. In the collision, the 2 astronauts push on each other so that Ann\"s final momentum is 
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come the left. What is Bob\"s last momentum?


Possible Answers:

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 to the left


 to the right


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 to the left


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 to the right


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 to the right


Correct answer:

 to the right


Explanation:

Apply conservation of momentum before and also after the collision.

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.

Taking left to it is in the an adverse direction, and also noting that Bob\"s initial momentum is 0 because he is at rest, we can use the noted information to check out that

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.

Solving for 

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, we get 
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. Because this price is positive, Bob\"s inert is in the confident direction (to the right).


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Example question #1 : inert


A

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 mass traveling to the appropriate on a two-dimensional Cartesian airplane at
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, ~ above a course inclined
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 to the hopeful x-axis, collides and sticks to a
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 mass travel to the left directly along the x-axis (no inclination) at
\"*\"
. What is the velocity and direction, v respect come the x-axis, the the combined body after the collision?


Possible Answers:

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 at 
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\"*\"
 at 
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 at 
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 at 
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 at 


Correct answer:

 at 


Explanation:

This is a fully inelastic collision, and, as with all collisions, it conserves straight momentum. To gain magnitude and also direction in two dimensions, it is typically finest to look in ~ the horizontal and vertical direction individually.

Horizontal direction: The

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 mass is moving to the appropriate at one inclination to the x-axis the
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. The horizontal component of its momentum is:

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The

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 mass is moving specifically to the left (no inclination), so its momentum is every in the horizontal direction, yet with a an unfavorable sign to indicate moving come the left on the Cartesian axes.

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So the complete x-momentum after ~ the collision is the sum of these two initial x-momenta, due to the fact that total inert is conserved in the collision.

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This instantly shows that the merged mass after the collision is relocating in the hopeful x-direction.

 

We now need to compute the final velocity in the x-direction. In this case:

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 is the total merged mass of
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 after the collision, and also we understand the final momentum, allowing us to settle for the last horizontal velocity.

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Vertical direction: The same procedure deserve to be applied to the y-direction. In this case, the process is simpler, because only the

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 mass contributes inert in the y-direction, and also that momentum will certainly be the exact same before and after the collision.

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Since the last momentum is now well-known to be positive in both the horizontal and vertical directions, the angle through respect come the x-axis need to be positive. Now, the last y-direction velocity have the right to be calculated.

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Final velocity: with the last velocity contents known, the final velocity deserve to be calculated from trigonometry.