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Ch 02: Motion Along a Straight Line
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경
2장, 문제 37

A juggler throws a bowling pin straight up with an initial speed of 8.208.20 m/s. How much time elapses until the bowling pin returns to the juggler's hand?

검증된 단계별 안내
1
Identify the key variables: initial velocity \( v_0 = 8.20 \) m/s, acceleration due to gravity \( g = 9.81 \) m/s² (acting downward), and final velocity \( v = 0 \) m/s at the peak of the throw.
Use the kinematic equation \( v = v_0 - gt \) to find the time \( t \) it takes for the bowling pin to reach its highest point. Set \( v = 0 \) and solve for \( t \).
Calculate the time to reach the peak using \( t = \frac{v_0}{g} \). This gives the time for the pin to stop rising.
Since the time to ascend is equal to the time to descend, multiply the time calculated in the previous step by 2 to find the total time for the pin to return to the juggler's hand.
Summarize the process: The total time elapsed is twice the time taken to reach the peak, which accounts for both the upward and downward journey of the bowling pin.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
5m
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주요 개념

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

Kinematics Equations

Kinematics equations describe the motion of objects without considering the forces that cause the motion. For an object thrown vertically, the key equation is: final velocity = initial velocity + (acceleration × time). In this scenario, the acceleration is due to gravity, which is approximately -9.81 m/s², acting downward.
추천 영상:
가이드 코스
08:25
Kinematics Equations

Free Fall Motion

Free fall motion refers to the movement of an object under the influence of gravitational force only. When the juggler throws the bowling pin upwards, it decelerates until it reaches its peak height, where the velocity is zero, and then accelerates back down. The time to reach the peak is equal to the time to return to the original position.
추천 영상:
가이드 코스
08:36
Vertical Motion & Free Fall

Symmetry of Projectile Motion

In projectile motion, especially vertical throws, the time taken to ascend to the highest point is equal to the time taken to descend back to the starting point. This symmetry helps in calculating the total time of flight by simply doubling the time taken to reach the peak height, which can be found using the initial velocity and gravitational acceleration.
추천 영상:
가이드 코스
04:27
Projectile Motion with Energy
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