Respuesta :
If a flea jumps straight up, and if air resistance is neglected (a rather poor approximation in this situation), how high does the flea go?
Answer;
=0.065 m or 65 mm
Explanation;
v = √(2as)
= √(2 * 1100m/s² * 0.00058 m) = 1.276 m/s
Therefore; initial velocity = 1.276 m/s
Then s = v² / 2g
g = 9.8 m/s²
= (1.276m/s)² / 19.6 m/s²
= 0.065 m or 65 mm
The distance over which a body accelerates is a determinant of how far the body can reach
The height to which the flea can jump is 6.558 cm
The reason the above value is correct is as follows;
Question: The parts of the question that appear missing could be;
Part A: How high can the flee jump, neglecting air resistance
The known parameters are;
The acceleration of the flea, a = 1100 m/s²
The distance over which the flee accelerates, s = 0.58 mm = 5.8 × 10⁻⁴ m
Method:
The initial velocity with which the flea leaves the ground is calculated, then with the value of the initial velocity, the height to which the flea jumps is found, and the distance of the acceleration is added to the height to give the total height
Solution:
The initial velocity with which the flea leaves the ground, v, is given as follows;
v² = u² + 2·a·s
Where;
u = The velocity with which the starts the acceleration = 0
∴ v² = 0 + 2 × 1,100 m/s² × 5.8 × 10⁻⁴ m = 1.276 m²/s²
v = √(1.276 m²/s²) = 1.1296017 m/s
The height to which the flea jumps from the height at which it leaves the ground, h, is given as follows;
v'² = v² - 2·g·h
v' = 0 = The final velocity at the maximum height
∴ 0² = v² - 2·g·h
v² = 2·g·h
h = v²/2·g
h = 1.1296017²/(2 × 9.81) ≈ 0.065
The total height to which the flea can jump, [tex]\mathbf{h_{max}}[/tex] = h + s
∴ [tex]h_{max}[/tex] = 0.065 + 5.8 × 10⁻⁴ = 0.06558
The total height to which the flea can jump, [tex]h_{max}[/tex] = 0.06558 m = 6.558 cm
The total height to which the flea can jump, [tex]h_{max}[/tex] = 6.558 cm
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