Question

A flea jumps straight up to a maximum height of 0.490 m . What is its initial velocity v0 as it leaves the ground? Express your answer in meters per second to three significant figures.

Answer 1

The initial velocity required for a flea to reach a maximum height of 0.490 m is determined using the kinematic equation for motion under gravity, resulting in an initial velocity of approximately 3.10 m/s.

Step-by-step explanation:

The student is asking about the initial velocity needed for a flea to reach a maximum height during its jump, which can be calculated using the principles of kinematics under the influence of gravity. The kinematics equation that relates initial velocity, maximum height, and acceleration due to gravity (which is approximately -9.81 m/s2 on Earth's surface) is represented by the following:

v2 = u2 + 2as, where:

• v is the final velocity (0 m/s at the maximum height)
• u is the initial velocity
• a is the acceleration due to gravity (-9.81 m/s2)
• s is the maximum height (0.490 m)

We rearrange the equation to solve for the initial velocity u:

u = sqrt(v2 - 2as)

Since the final velocity v at maximum height is 0 m/s, the initial velocity can be determined:

u = sqrt(0 - (2 * (-9.81) * 0.490))

The calculation yields:

u = sqrt(19.62 * 0.490)

u ≈ 3.096 m/s

The initial velocity of the flea as it leaves the ground is approximately 3.10 m/s to three significant figures.