a 20.0 kg child on an 80 kg boat throws a 5 kg package horizontally with a speed of 10 m/s. Calculate the resulting density of the boat, assuming it was initially set at rest.
Density? What was the original volume? Assuming the density of the boat to be originally about .50, then
volume= 105kg/.5=210liters
Then new density is 100kg/210liters=.476
To calculate the resulting density of the boat, we first need to find the total mass of the system (child + boat + package) and then divide it by the volume of the boat.
Let's start by finding the total mass of the system:
Total mass = mass of child + mass of boat + mass of package
Given:
Mass of child (m₁) = 20.0 kg
Mass of boat (m₂) = 80.0 kg
Mass of package (m₃) = 5.0 kg
Total mass (m_total) = m₁ + m₂ + m₃
Next, we need to find the velocity of the boat after the child throws the package. Since the child and the boat are initially at rest, the momentum before and after the throw should be conserved.
Before the throw:
Momentum of child + Momentum of boat = 0
After the throw:
Momentum of child + Momentum of boat + Momentum of package = 0
The momentum of an object is given by the product of its mass and velocity: Momentum = mass × velocity.
Before the throw:
0 = m₁ × 0 + m₂ × 0
After the throw:
0 = m₁ × 0 + m₂ × v + m₃ × v
Since the child throws the package horizontally with a speed of 10 m/s, the momentum of the package and boat will be in the same direction.
Applying the conservation of momentum, we can equate the momentum terms:
0 = (m₂ + m₃) × v
Solving for v:
v = 0
The velocity of the boat after the throw is 0 m/s. This means the boat remains at rest.
Now that we have the total mass (m_total) and the volume of the boat, we can calculate the density.
Density (ρ) = mass (m_total) / volume (V)
However, we don't have the volume of the boat given in the problem statement. Without the volume, we cannot directly calculate the density of the boat. It's possible that some additional information is missing in the problem.