Answer:
A flea can attain a maximum elevation of 51 mm.
Explanation:
Hello!
The following equations describe the height and velocity of the flea:
During the jump:
h = h0 + v0 · t + 1/2 · a · t²
v = v0 + a · t
In free fall:
h = h0 + v0 · t + 1/2 · g · t²
v = v0 + g · t
Where:
h = flea's height at time t.
h0 = initial height.
v0 = starting velocity.
t = time interval.
a = flea's acceleration while jumping.
v = flea's velocity at that specific time.
g = gravitational acceleration.
Initially, we need to determine the time taken for the flea to attain a height of 0.0005 m. This will help us calculate the flea's velocity during the jump:
h = h0 + v0 · t + 1/2 · a · t²
If we assume the ground as the origin, thus h0 = 0. Since the flea starts stationary, v0 = 0. Therefore:
h = 1/2 · a · t²
We need to find the value of t when h = 0.0005 m:
0.0005 m = 1/2 · 1000 m/s² · t²
0.0005 m / 500 m/s² = t²
t = 0.001 s
Next, we calculate the velocity achieved during that time:
v = v0 + a · t (v0 = 0)
v = a · t
v = 1000 m/s² · 0.001 s
v = 1.00 m/s
At a height of 0.50 mm, the flea's velocity stands at 1.00 m/s. This initial speed will reduce due to gravity's downward pull. When the speed reaches zero, the flea will have reached its peak height. Using the velocity equation, let's determine the time taken to reach maximum height (v = 0):
v = v0 + g · t
At peak height, v = 0:
0 m/s = 1.00 m/s - 9.81 m/s² · t
-1.00 m/s / -9.81 m/s² = t
t = 0.102 s
Now, we can compute the height attained by the flea during this time:
h = h0 + v0 · t + 1/2 · g · t²
h = 0.0005 m + 1.00 m/s · 0.102 s - 1/2 · 9.81 m/s² · (0.102 s)²
h = 0.051 m
A flea reaches a maximum height of 51 mm.
