A 70.3-kg person puts on a life jacket, jumps into the water, and floats. The jacket has a volume of 3.07 x 10-2 m3 and is completely submerged under the water. The volume of the person's body that is underwater is 6.49 x 10-2 m3. What is the density of the life jacket?

M = 70.3 kg = Mass of the person.

Dj = Density of the jacket.
Vj = 0.0307 m^3 = Vol. of the jacket.
Dp = Density of the person.
Vp = 0.0649 m^3 = Vol. of the person.
Dw = 1000kg/m^3 = Density of water.

Mj+Mp = (Vj+Vp) * Dw
Mj+Mp = 0.0956m^3 * 1000kg/m^3=95.6 kg
Mj = 95.6 - Mp = 95.6 - 70.3 = 25.3 kg

Dj = Mj/Vj = 25.3/0.0956=264.6 kg/m^3 =
Density of the jacket.

To find the density of the life jacket, we need to first calculate the buoyant force acting on it. The buoyant force is equal to the weight of the fluid displaced by the object, according to Archimedes' principle.

1. First, let's calculate the weight of the fluid displaced by the life jacket. We can find this using the formula:

Weight of fluid displaced = density of fluid × volume of fluid displaced

2. Since the life jacket is completely submerged underwater, the fluid being displaced is water. The density of water is approximately 1000 kg/m3.

Weight of fluid displaced = 1000 kg/m3 × volume of fluid displaced

3. The volume of the fluid displaced is equal to the volume of the life jacket, which is given as 3.07 x 10-2 m3.

Weight of fluid displaced = 1000 kg/m3 × 3.07 x 10-2 m3

4. Next, let's calculate the buoyant force acting on the life jacket. The buoyant force is equal to the weight of the fluid displaced.

Buoyant force = Weight of fluid displaced = 1000 kg/m3 × 3.07 x 10-2 m3

5. Now, we can calculate the net force acting on the life jacket. The net force is the difference between the weight of the person (70.3 kg) and the buoyant force acting upwards.

Net force = weight of the person - buoyant force

Net force = 70.3 kg × 9.8 m/s2 - (1000 kg/m3 × 3.07 x 10-2 m3 × 9.8 m/s2)

6. Finally, the density of the life jacket can be calculated using the formula:

Density = mass / volume

Density = (weight of the person - net force) / volume of the life jacket

Density = (70.3 kg × 9.8 m/s2 - net force) / 3.07 x 10-2 m3

Plug in the value of the net force calculated in step 5 to get the final answer.