A rocket, 8975 kg, traveling at 1255 m/s East explodes into two pieces. if one piece, 2450 kg, moves at 750.0 m/s due south, what is:
the mass of the second piece?
the momentum of the second piece?
the velocity of the second piece?
To solve this problem, let's first calculate the momentum of the first piece before the explosion.
1. Momentum of the first piece before the explosion:
Momentum = mass × velocity
Momentum = 8975 kg × 1255 m/s (East)
Momentum = 1.1271875 × 10^7 kg·m/s (East)
Now, we can use the conservation of momentum principle to find the momentum of the second piece.
2. Momentum of the second piece:
According to the conservation of momentum, the total momentum before the explosion is equal to the total momentum after the explosion.
Momentum_before = Momentum_after
Momentum_before = 1.1271875 × 10^7 kg·m/s (East)
Now, we need to find the momentum of the second piece after the explosion.
Momentum_after = mass_secondPiece × velocity_secondPiece
Substituting the given values:
1.1271875 × 10^7 kg·m/s (East) = mass_secondPiece × velocity_secondPiece
To find the mass of the second piece, we need to divide both sides of the equation by the velocity of the second piece.
mass_secondPiece = (1.1271875 × 10^7 kg·m/s) / (velocity_secondPiece)
To find the velocity of the second piece, we need to solve for it using the given mass and velocity of the first piece.
3. Velocity of the second piece:
Momentum_before = Momentum_after
mass_firstPiece × velocity_firstPiece = mass_secondPiece × velocity_secondPiece
Substituting the given values:
(8975 kg × 1255 m/s) = (mass_secondPiece) × (velocity_secondPiece)
Divide both sides of the equation by the mass of the second piece to solve for the velocity_secondPiece:
velocity_secondPiece = (8975 kg × 1255 m/s) / (mass_secondPiece)
Now, we have two equations to solve for the mass of the second piece and its velocity. Let's calculate them step-by-step.
First, let's solve for the mass of the second piece:
mass_secondPiece = (1.1271875 × 10^7 kg·m/s) / (velocity_secondPiece)
And then, let's solve for the velocity of the second piece:
velocity_secondPiece = (8975 kg × 1255 m/s) / (mass_secondPiece)
To solve this problem, we can use the principle of conservation of momentum. According to the principle, the total momentum before the explosion is equal to the total momentum after the explosion.
1. Finding the mass of the second piece:
Let's assume the mass of the second piece is m2. The total mass before the explosion is given as 8975 kg, and the mass of the first piece after the explosion is given as 2450 kg. Therefore, the mass of the second piece can be calculated by subtracting the mass of the first piece from the total mass:
m2 = total mass - mass of first piece
m2 = 8975 kg - 2450 kg
m2 = 6525 kg
So, the mass of the second piece is 6525 kg.
2. Finding the momentum of the second piece:
The momentum of an object is given by the product of its mass and velocity. We already have the mass of the second piece (m2). To find its momentum, we need to know its velocity.
Unfortunately, the problem doesn't provide the velocity of the second piece directly. However, we can use the principle of conservation of momentum to find it.
Before the explosion, the rocket's momentum is given as:
momentum before = (mass of first piece) x (initial velocity of the rocket)
After the explosion, the momentum of the first piece is given as:
momentum of first piece = (mass of first piece) x (velocity of first piece)
The momentum of the second piece is given as:
momentum of second piece = (mass of second piece) x (velocity of second piece)
Using the conservation of momentum principle, we can equate the total initial momentum to the total momentum after the explosion:
momentum before = momentum of first piece + momentum of second piece
(mass of rocket) x (initial velocity of the rocket) = (mass of first piece) x (velocity of first piece) + (mass of second piece) x (velocity of second piece)
Substituting the given values, we have:
8975 kg x 1255 m/s = 2450 kg x 750.0 m/s + 6525 kg x (velocity of second piece)
Solving this equation for the velocity of the second piece results in:
velocity of second piece = (8975 kg x 1255 m/s - 2450 kg x 750.0 m/s) / 6525 kg
Calculating this expression, we find the velocity of the second piece:
velocity of second piece = 1430.0 m/s
So, the velocity of the second piece is 1430.0 m/s.
3. Finding the velocity of the second piece:
As calculated above, the velocity of the second piece is 1430.0 m/s.
To summarize:
- The mass of the second piece is 6525 kg.
- The momentum of the second piece is calculated by multiplying the mass of the second piece (6525 kg) with its velocity.
- The velocity of the second piece is 1430.0 m/s.