If the flea jumps straight up to a height of 0.670 m, it will be in the air 0.74 s.
The time that the flea will be in the air is given by the sum of the rise time and the fall time, which are the same:
[tex] t_{t} = t_{r} + t_{f} = 2t [/tex] (1)
Where:
[tex] t_{t} [/tex]: is the total time
[tex] t_{r} [/tex]: is the rise time = [tex] t_{f} [/tex] (the fall time) = t
To calculate the rise time, and so the fall time, we can use the following equation:
[tex] v_{f} = v_{i} - gt [/tex] (2)
Where:
[tex] v_{f} [/tex]: is the final velocity = 0 (at the maximum height)
[tex] v_{i}[/tex]: is the initial velocity
g: is the acceleration due to gravity = 9.81 m/s²
First, we need to find the initial velocity. We can use the equation:
[tex] v_{f}^{2} = v_{i}^{2} - 2gh [/tex] (3)
Where:
h: is the maximum height = 0.670 m
Hence, the initial velocity is (eq 3):
[tex] v_{i} = \sqrt{2gh} = \sqrt{2*9.81 m/s^{2}*0.670 m} = 3.63 m/s [/tex]
Now, the rise and fall time is (eq 2):
[tex] t = \frac{v_{i}}{g} = \frac{3.63 m/s}{9.81 m/s{2}} = 0.37 s [/tex]
Finally, the total time is (eq 1):
[tex] t_{t} = (0.37*2) s = 0.74 s [/tex]
Therefore, the flea is in the air 0.74 s.
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