If a flea can jump straight up to a height of 0.4400.440 m, How long is it in the air?

Ch 02: Motion Along a Straight Line

Young & Freedman Calc - University Physics 15th Edition

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Young & Freedman Calc 15th Edition

Ch 02: Motion Along a Straight Line

문제 31b

2장, 문제 31b

If a flea can jump straight up to a height of $0.440$ m, How long is it in the air?

검증된 단계별 안내

Identify the known values: the maximum height (h) the flea can reach is 0.440 m, and the acceleration due to gravity (g) is approximately 9.81 m/s² downward.

Use the kinematic equation for vertical motion to find the time to reach the maximum height: $ v_f = v_i + a t $, where $ v_f $ is the final velocity (0 m/s at the top), $ v_i $ is the initial velocity, $ a $ is the acceleration (-9.81 m/s²), and $ t $ is the time to reach the maximum height.

Rearrange the equation to solve for the initial velocity $ v_i $: $ v_i = v_f - a t $. Since $ v_f = 0 $ at the maximum height, $ v_i = -(-9.81) t $.

Use another kinematic equation to relate the initial velocity to the maximum height: $ h = v_i t + \frac{1}{2} a t^2 $. Substitute $ v_i $ from the previous step and solve for $ t $.

The total time the flea is in the air is twice the time to reach the maximum height, as the time to ascend and descend are equal. Calculate the total time using $ t_{total} = 2t $.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

Projectile Motion

Projectile motion refers to the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. In this context, the flea's jump can be analyzed as a vertical projectile motion, where the initial velocity, maximum height, and time of flight are key parameters.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. For vertical motion, the equation h = v_i * t + 0.5 * g * t^2 can be used, where h is the height, v_i is the initial velocity, g is the acceleration due to gravity, and t is the time. These equations help determine the time the flea is in the air.

Acceleration Due to Gravity

The acceleration due to gravity (g) is approximately 9.81 m/s² on Earth. It acts downward, affecting the motion of all objects in free fall. Understanding this constant is crucial for calculating the time of flight and other parameters in projectile motion problems, such as the flea's jump.