Questions: In this problem, you will apply kinematic equations to a jumping flea. Take the magnitude of free-fall acceleration to be 9.80 m / s^2. Ignore air resistance. A flea jumps straight up to a maximum height of 0.410 m. What is its initial velocity v0 as it leaves the ground? Express your answer in meters per second to three significant figures.

Solution Steps

• Maximum height ($h$) = 0.410 m
• Acceleration due to gravity ($g$) = $9.80 \, \mathrm{m/s^2}$
• Final velocity at maximum height ($v$) = 0 m/s (since the flea momentarily stops at the peak)

Use the kinematic equation that relates initial velocity, final velocity, acceleration, and displacement: $$v^2 = v_{0}^2 + 2a s$$ where:

• $v$ is the final velocity,
• $v_{0}$ is the initial velocity,
• $a$ is the acceleration,
• $s$ is the displacement.

Substitute $v = 0 \, \mathrm{m/s}$, $a = -9.80 \, \mathrm{m/s^2}$ (negative because gravity acts downward), and $s = 0.410 \, \mathrm{m}$: $$0 = v_{0}^2 + 2(-9.80)(0.410)$$

Rearrange the equation to solve for $v_{0}^2$: $$v_{0}^2 = -2(-9.80)(0.410)$$ $$v_{0}^2 = 2 \times 9.80 \times 0.410$$ $$v_{0}^2 = 8.036$$

Take the square root to find $v_{0}$: $$v_{0} = \sqrt{8.036}$$ $$v_{0} \approx 2.835 \, \mathrm{m/s}$$

Final Answer