In this problem, you will apply kinematic equations to a jumping flea. Take the magnitude of free-fall acceleration to be 9.80 m/s2
 . Ignore air resistance.How long is the flea in the air from the time it jumps to the time it hits the ground?
Express your answer in seconds to three significant figures.

To solve this problem, we will apply the kinematic equations for vertical motion under the influence of gravity. Since the flea jumps up and eventually returns to the ground, the total time of flight is twice the time it takes for the flea to reach its maximum height.

### Kinematic equation for upward motion:
The equation for the upward motion is given by:
\[
v_f = v_i + a t
\]
where:
- \( v_f = 0 \) (velocity at the highest point is zero),
- \( v_i \) is the initial upward velocity,
- \( a = -9.80 \, \text{m/s}^2 \) (negative because gravity opposes the upward motion),
- \( t \) is the time to reach the maximum height.

Rearranging the equation to solve for \( t \), we get:
\[
t_{\text{up}} = \frac{v_i}{9.80}
\]

The total time of flight is double this value because the time to go up is equal to the time to come down. So, the total time \( T \) is:
\[
T = 2 \times t_{\text{up}} = \frac{2v_i}{9.80}
\]

To express the total time of flight, we need the initial velocity \( v_i \). If the problem provides the initial velocity or the height of the flea's jump, we can substitute it into the equation and calculate the time of flight.

Could you provide the initial velocity or maximum height, so I can complete the calculation?

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. How long is the flea in the air from the time it jumps to the time it hits the ground? Express your answer in seconds to three significant figures.

Solve the jumping flea problem using kinematic equations. Learn how to calculate the time of flight for a flea in free fall under the influence of gravity, using concepts of kinematics and the symmetry of motion. Ideal for students in Grades 9-12.

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