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Answer :
After calculating Darin's weight and considering the upward air resistance, we find the net force and use Newton's Second Law to calculate his downward acceleration, resulting in an acceleration of -8.12 m/s².
To determine Darin's acceleration when his 75.5-kg body experiences +128 N of air resistance upward, we can use Newton's Second Law of Motion. The law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
Firstly, we calculate Darin's weight, which is the force due to gravity acting on his mass:
- Weight (force due to gravity) = mass × acceleration due to gravity
- Weight = 75.5 kg × 9.8 m/s²
- Weight = 740.9 N (downward)
Next, we find the net force by subtracting the air resistance from Darin's weight, since air resistance acts upward:
- Net force = Weight - air resistance
- Net force = 740.9 N - 128 N
- Net force = 612.9 N (downward)
Finally, we can calculate Darin's acceleration:
- Net force = mass × acceleration
- 612.9 N = 75.5 kg × acceleration
- Acceleration = 612.9 N / 75.5 kg
- Acceleration = 8.12 m/s² (downward)
Since the question specifies acceleration will be negative due to the downward direction, Darin's acceleration at this instant is -8.12 m/s².
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