A supertanker with the mass of 5.55 × 108 kg is moving with a constant velocity. Its engines generate a forward thrust of 4.55 × 105 N. Determine (a) the magnitude of the resistive force exerted on the tanker by the water and (b) the magnitude of the upward buoyant force exerted on the tanker by the water.

To determine the magnitude of the resistive force exerted on the tanker by the water, we can use Newton's first law of motion, which states that an object will remain in a state of rest or move with constant velocity unless acted upon by a net external force. In this case, the resistive force acts as the net external force opposing the motion of the tanker.

(a) To find the magnitude of the resistive force, we can use the equation:

Net Force = Mass × Acceleration

Since the tanker is moving with a constant velocity, the acceleration is zero. Therefore, the net force acting on the tanker is also zero. The thrust exerted by the engines is equal in magnitude but opposite in direction to the resistive force exerted by the water.

Hence, the magnitude of the resistive force exerted on the tanker by the water is 4.55 × 105 N.

(b) To determine the magnitude of the upward buoyant force exerted on the tanker by the water, we can use Archimedes' principle, which states that the buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.

The buoyant force can be calculated using the equation:

Buoyant Force = Weight of Fluid Displaced

Since the tanker is floating in water, the weight of the water displaced is equal to the weight of the tanker itself (according to Archimedes' principle). Thus, the magnitude of the upward buoyant force exerted on the tanker by the water is equal to its weight.

To calculate the weight, we use the equation:

Weight = Mass × Gravity

where the mass of the tanker is given as 5.55 × 108 kg and the acceleration due to gravity is approximately 9.8 m/s^2.

Therefore, the magnitude of the upward buoyant force exerted on the tanker by the water is (5.55 × 108 kg) × (9.8 m/s^2).

To determine the magnitude of the resistive force exerted on the tanker by the water (Fr), we can use Newton's second law of motion.

The equation Fnet = m × a can be rearranged to solve for the resistive force:

Fnet = Fr - Ff = m × a

Where:
- Ff represents the force of friction acting on the tanker
- m is the mass of the tanker
- a is the acceleration of the tanker, which is zero because it is moving with a constant velocity

Substituting the given values:
- Fnet = 4.55 × 10^5 N
- m = 5.55 × 10^8 kg
- a = 0

We have:
4.55 × 10^5 N = Fr - Ff

Since the tanker is moving with a constant velocity, the net force is zero. Hence:

Fr = Ff

Therefore, the magnitude of the resistive force exerted on the tanker by the water is 4.55 × 10^5 N.

To determine the magnitude of the upward buoyant force exerted on the tanker by the water (Fb), we can use Archimedes' principle.

The buoyant force is equal to the weight of the fluid displaced by the object. It can be calculated using the formula:

Fb = ρ × g × V

Where:
- ρ is the density of the fluid, which in this case is water (approximately 1000 kg/m^3)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- V is the volume of water displaced by the tanker

To calculate V, we can use the formula:

V = m / ρ

Substituting the given values:
- m = 5.55 × 10^8 kg
- ρ = 1000 kg/m^3

We can calculate V:
V = (5.55 × 10^8 kg) / (1000 kg/m^3) = 5.55 × 10^5 m^3

Now, substituting the known values back into the first equation:
Fb = (1000 kg/m^3) × (9.8 m/s^2) × (5.55 × 10^5 m^3)

We can calculate:
Fb = 5.43 × 10^9 N

Therefore, the magnitude of the upward buoyant force exerted on the tanker by the water is 5.43 × 10^9 N.