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Ch 08: Momentum, Impulse, and Collisions
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경
8장, 문제 40a

To protect their young in the nest, peregrine falcons will fly into birds of prey (such as ravens) at high speed. In one such episode, a 600-g falcon flying at 20.0 m/s hit a 1.50-kg raven flying at 9.0 m/s. The falcon hit the raven at right angles to its original path and bounced back at 5.0 m/s. (These figures were estimated by the author as he watched this attack occur in northern New Mexico.) By what angle did the falcon change the raven's direction of motion?

검증된 단계별 안내
1
Convert the masses of the falcon and the raven into kilograms for consistency in SI units. The falcon's mass is 600 g, which is equivalent to 0.600 kg. The raven's mass is already given as 1.50 kg.
Apply the principle of conservation of momentum. Since the collision occurs in two dimensions, break the momentum into x and y components. Write the momentum conservation equations for both components: For the x-direction: mfvf,x + mrvr,x = mfvf,x' + mrvr,x' For the y-direction: mfvf,y + mrvr,y = mfvf,y' + mrvr,y'
Substitute the known values into the momentum conservation equations. For the initial velocities: - The falcon's initial velocity is 20.0 m/s in the x-direction, so vf,x = 20.0 m/s and vf,y = 0. - The raven's initial velocity is 9.0 m/s in the y-direction, so vr,x = 0 and vr,y = 9.0 m/s. - After the collision, the falcon's velocity is 5.0 m/s in the negative x-direction, so vf,x' = -5.0 m/s and vf,y' = 0.
Solve the momentum conservation equations for the raven's final velocity components (vr,x' and vr,y'). Use the equations derived in step 2 and the substituted values from step 3. This will give you the x and y components of the raven's final velocity.
Determine the angle by which the raven's direction of motion changes. Use the arctangent function to calculate the angle: θ = tan-1(vr,y' / vr,x'). Ensure that you account for the correct quadrant based on the signs of vr,x' and vr,y'.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
13m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Momentum Conservation

Momentum conservation is a fundamental principle in physics stating that the total momentum of a closed system remains constant if no external forces act on it. In collisions, the momentum before the event equals the momentum after, allowing us to analyze the effects of the collision on the involved objects. This concept is crucial for solving problems involving moving bodies, such as the falcon and raven in this scenario.
추천 영상:
가이드 코스
05:58
Conservation Of Momentum

Vector Components

In physics, vectors represent quantities that have both magnitude and direction, such as velocity. To analyze motion in two dimensions, it's essential to break down vectors into their components along the x and y axes. This method allows for easier calculations of angles and resultant velocities, which is necessary for determining how the falcon's collision affects the raven's trajectory.
추천 영상:
가이드 코스
07:30
Vector Addition By Components

Collision Angles

Collision angles refer to the angles at which two objects collide, significantly influencing their post-collision paths. In this scenario, understanding the angle at which the falcon strikes the raven and how it alters the raven's direction is key to solving the problem. Analyzing the change in direction involves applying trigonometric principles to the vectors representing the velocities of both birds.
추천 영상:
가이드 코스
06:21
Collisions with Springs
관련 실천
교과서 질문

To protect their young in the nest, peregrine falcons will fly into birds of prey (such as ravens) at high speed. In one such episode, a 600-g falcon flying at 20.0 m/s hit a 1.50-kg raven flying at 9.0 m/s. The falcon hit the raven at right angles to its original path and bounced back at 5.0 m/s. (These figures were estimated by the author as he watched this attack occur in northern New Mexico.) What was the raven's speed right after the collision?

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교과서 질문

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교과서 질문

Two fun-loving otters are sliding toward each other on a muddy (and hence frictionless) horizontal surface. One of them, of mass 7.50 kg, is sliding to the left at 5.00 m/s, while the other, of mass 5.75 kg, is slipping to the right at 6.00 m/s. They hold fast to each other after they collide. Find the magnitude and direction of the velocity of these free-spirited otters right after they collide.

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