Answer :
The diver's acceleration is approximately 1.01 m/s^2.
To calculate the diver's acceleration, we need to consider the forces acting on the diver.
1. Weight force: The weight force acts downward and is given by the formula:
Weight = mass × gravity
= 93 kg × 9.8 m/s^2
= 911.4 N
2. Buoyant force: When the diver inhales to have a body density less than the surrounding water, there will be an upward buoyant force acting on the diver. The buoyant force is given by:
Buoyant force = fluid density × volume submerged × gravity
The volume submerged is equal to the volume of the diver. Since the diver's body density is 948 kg/m^3, we can calculate the volume submerged as:
Volume submerged = mass / body density
= 93 kg / 948 kg/m^3
= 0.0979 m^3
Now we can calculate the buoyant force:
Buoyant force = 1024 kg/m^3 × 0.0979 m^3 × 9.8 m/s^2
= 1005.5 N
Now, let's calculate the net force acting on the diver:
Net force = Buoyant force - Weight
= 1005.5 N - 911.4 N
= 94.1 N
Since the diver is floating to the surface, the net force is directed upward. We can use Newton's second law to calculate the acceleration:
Net force = mass × acceleration
Rearranging the formula, we find:
Acceleration = Net force / mass
= 94.1 N / 93 kg
≈ 1.01 m/s^2
Therefore, the diver's acceleration is approximately 1.01 m/s^2.
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