If a flea can jump straight up to a height of 0.4400.440 m, what is its initial speed as it leaves the ground?

Ch 02: Motion Along a Straight Line

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 02: Motion Along a Straight Line

Problema 35a

Capitolo 2, Problema 35a

If a flea can jump straight up to a height of $0.440$ m, what is its initial speed as it leaves the ground?

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Identify the known values: the maximum height (h) the flea can jump 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 that relates initial velocity (v₀), final velocity (v), acceleration (a), and displacement (s): v² = v₀² + 2as. Here, the final velocity (v) at the maximum height is 0 m/s, the displacement (s) is 0.440 m, and the acceleration (a) is -9.81 m/s² (negative because it acts downward).

Rearrange the equation to solve for the initial velocity (v₀): v₀² = v² - 2as. Substitute the known values into the equation: v₀² = 0 - 2(-9.81 m/s²)(0.440 m).

Calculate the expression inside the square root: v₀² = 2 * 9.81 m/s² * 0.440 m.

Take the square root of the result to find the initial speed (v₀) of the flea as it leaves the ground.

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Kinematics Equations

Kinematics equations describe the motion of objects without considering the forces that cause the motion. For vertical motion, the equation v^2 = u^2 + 2as can be used, where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity, and s is the displacement. This equation helps determine the initial speed of the flea.

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Kinematics Equations

Gravitational Acceleration

Gravitational acceleration is the acceleration of an object due to Earth's gravity, approximately 9.81 m/s² downward. It is crucial for calculating the motion of objects in free fall or vertical jumps, like the flea's jump, as it affects the velocity and displacement during the motion.

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Energy Conservation

Energy conservation in physics states that energy cannot be created or destroyed, only transformed. In the context of the flea's jump, the kinetic energy at the start is converted into potential energy at the peak height. This principle helps relate the initial speed to the maximum height reached by the flea.

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