Answer
given,
height of the jump = 0.44 m
acceleration due to gravity, g = 9.8 m/s²
velocity at the height point = 0 m/s
initial speed = ?
Using equation of motion for speed calculation
v² = u² + 2 g h
0 = u² - 2 x 9.8 x 0.44
u = √8.624
u = 2.94 m/s
time taken to reach the highest point
v = u + g t
0 = 2.94 - 9.8 x t
t = 0.3 s
total time of flight will be equal to double of the time taken to reach the maximum height.
Total time = 2 x 0.3 = 0.6 s
A flea jumps straight up to a height of 0.440 m with an initial speed of 2.94 m/s and is in the air for 0.600 s.
A flea jumps straight up to a height (h) of 0.440 m. At the maximum height, the final speed (v) is zero. Given that the gravity (g) is 9.81 m/s², we can calculate the initial speed (u) using the following kinematic expression (We will assume y+ as the positive direction)
[tex]v^{2} = u^{2} + 2 \times g \times h \\\\(0m/s)^{2} = u^{2} + 2 \times (-9.81m/s^{2} ) \times 0.440m\\\\u = 2.94 m/s[/tex]
We can calculate the time (t) required to reach the maximum height using the following kinematic expression.
[tex]v = u + g \times t\\\\0m/s = 2.94m/s - 9.81m/s^{2} \times t\\\\t = 0.300 s[/tex]
The time in the air will be double the time to reach the maximum height.
[tex]t_{total} = 2 \times 0.300 s = 0.600 s[/tex]
A flea jumps straight up to a height of 0.440 m with an initial speed of 2.94 m/s and is in the air for 0.600 s.
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