Concept explainers
(a)
The direction should aim to reach the banana into the monkey’s hand.
(a)
Answer to Problem 110P
The direction should aim to reach the banana into the monkey’s hand is
Explanation of Solution
The vertical distance from the monkey’s hand to the person hand is
Write the expression to calculate the direction.
Here,
Substitute
Conclusion:
Therefore, the direction should aim to reach the banana into the monkey’s hand is
(b)
The reason for why the direction is same for different values of the banana’s launching speed.
(b)
Answer to Problem 110P
The launching speed is independent of the direction since both monkey and banana would have same downward acceleration.
Explanation of Solution
As the banana throws from the person’s hand, the acceleration on the banana is downward and is equal to the acceleration due to gravity of earth. In the case of monkey, the same downward acceleration would feel on the monkey.
Thus, the downward displacement of the monkey and banana is same with a magnitude of
(c)
The initial speed of the banana.
(c)
Answer to Problem 110P
The initial speed of the banana is
Explanation of Solution
The distance from the monkey to banana is
Write the expression to calculate the time required to travel the distance.
Substitute
Write the expression to calculate the initial speed of the banana.
Here, v is the initial speed of the banana.
Substitute
Conclusion:
Therefore, the initial speed of the banana is
(d)
The magnitude of distance d.
(d)
Answer to Problem 110P
The magnitude of d is
Explanation of Solution
The mass of the banana is
Write expression for the conservation of momentum along horizontal direction.
Here, m is the mass of the banana, M is the mass of the monkey, V is the final speed of the monkey along horizontal direction.
Rewrite the above expression in terms of V.
Substitute
Write the expression for the conservation of momentum in vertical direction.
Here,
Rewrite the above equation in terms of
Write the expression to calculate
Use the above expression in (II) to rewrite.
Substitute
Write the expression for the time taken by the monkey to hit the ground.
Here,
Substitute
The above equation is the quadratic form. Solve the above equation using quadratic formula to calculate
Write the expression to calculate the horizontal distance d.
Substitute
Conclusion:
Therefore, the magnitude of d is
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