Final answer:
The direction of the flea's acceleration is found by calculating both vertical and horizontal accelerations and then using trigonometry to determine the angle relative to the vertical.
Step-by-step explanation:
The question is about finding the direction of the acceleration of a flea relative to the vertical when it exerts a force downward and is simultaneously affected by a horizontal force due to the breeze. This is a classic physics problem involving Newton's Second Law of motion. First, we identify the forces: the flea exerts a force of 12 × 10−5 N downward, and the breeze exerts a force of 0.52 × 10−6 N horizontally. We calculate the acceleration in both directions, and then use trigonometry to find the direction θ relative to the vertical.
To calculate the acceleration caused by the vertical force, we account for gravity by subtracting the flea's weight from the exerted force:
- Weight of flea (w) = mass (m) × gravity (g) = 6 × 10−7 kg × 9.81 m/s2
- Net vertical force = exerted force − weight = 12 × 10−5 N − w
- Vertical acceleration (ay) = net vertical force / m
The horizontal acceleration (ax) is simply the horizontal force divided by mass:
- Horizontal acceleration (ax) = breeze force / m
To find θ, we use:
- tan θ = ax / ay
- θ = arctan(ax / ay)
Note that you need to find actual values of vertical and horizontal accelerations, which are not calculated in this example.