In the preceding question, in which case is the greatest impulse required?
The greatest impulse required in the given conditions.
Answer to Problem 12TE
The baseball will undergo the greatest impulse if it is caught and then thrown back.
Explanation of Solution
Write the expression for the change in momentum.
Here,
Pf is the final momentum
Pi is the initial momentum
Substitute mv for Pf and mv2 for Pi in the above equation.
…… (I)
From previous question, consider the third case in which the baseball is first caught and then thrown back with an initial velocity v and final velocity is -v .
Substitute v for vi and -v for v2 in equation (I).
From the above results, it is clear that the ball will undergo the greatest change in momentum if it is caught and then thrown back, which is twice as much as the change in momentum when ball is either caught or thrown.
Impulse is equal to change in momentum. So, the maximum impulse will be required to impart greatest change in momentum of the baseball. Therefore maximum impulse needs to be imparted to the baseball when it is caught and then thrown back.
Conclusion:
Therefore, the baseball will undergo the greatest impulse if it is caught and then thrown back.
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