Answer:
The acceleration will be 18 m/s², 6° from the vertical.
Explanation:
The resulting force will be the sum of both forces (see figure):
F flea = (0, 1.07 × 10⁻⁵ N)
F wind = (1.12 × 10⁻⁶ N, 0)
Resulting force = F flea + F wind
R F = (0, 1.07 × 10⁻⁵ N) + (1.12 × 10⁻⁶ N, 0) = ( 1.12 × 10⁻⁶ N, 1.07 × 10⁻⁵ N)
The magnitude of the resulting force will be:
[tex]|RF| = \sqrt{(1.12 * 10^{-6} N)^{2} + (1.07* 10^{-5} N)^{2}} = 1.08 * 10^{-5} N[/tex]
The magnitude of the acceleration will be:
F = m·a
Where
F = force
m = mass
a = acceleration
F/m = a
1.08 × 10 ⁻⁵N / 6.0 × 10⁻⁷ kg = 18 m/s²
The direction of the acceleration will be the same as the direction of the resulting force. Using trigonometry:
cos α = adjacent/hypotenuse = 1.12 × 10⁻⁶ N / 1.08 × 10⁻⁵ N
α = 84°
Then the acceleration will be:
18 m/s² (90° - 84°) 6° from the vertical.
The direction and magnitude of acceleration will be 18 m/s², 6° from the vertical.
Acceleration is given by the ratio of Resultant or total force acting on any object and the its mass.
The resulting force will be the sum of both forces.
Force exerted when flea jumps is 1.07 × 10⁻⁵ N and Force of wind is 1.12 × 10⁻⁶ N, then the resulting force will be
R =sq rt [(Fflea)² + (Fwind)²]
R = 1.08 × 10 ⁻⁵N
If the mass of flea is 6.0 × 10⁻⁷ kg, then the magnitude of the acceleration will be
a =F/m
a =1.08 × 10 ⁻⁵N / 6.0 × 10⁻⁷ kg
a = 18 m/s²
The direction of the acceleration will be the same as the direction of the resulting force.
cos α = 1.12 × 10⁻⁶ N / 1.08 × 10⁻⁵ N
α = 84°
Direction is (90° - 84°) = 6° from the vertical.
Thus, the direction and magnitude of acceleration will be 6° and 18 m/s².
Learn more about acceleration.
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