a 5 kg fish swimming at a speed of 1m/s swallows an absent minded 1 kg fish swimming toward it at 4 m/s. the speed of the larger fish after lunch is?
Instantly after the "collision", you can apply the law of conservation of momentum, but shortly afterwards the speed will change if large fish continues to swim.
(5 kg * 1 m/s) + (1 kg * -4 m/s) = 6 kg * Vfinal
Vfinal = 1/6 m/s
Well, looks like the 5 kg fish will have a "whale" of a time digesting that 1 kg fish! But, to answer your question, let's calculate the momentum before and after the interaction.
The momentum of an object is given by the equation p = m * v, where p is momentum, m is the mass, and v is the velocity.
Before lunch, the momentum of the 5 kg fish is (5 kg) * (1 m/s) = 5 kg⋅m/s.
The momentum of the 1 kg fish is (1 kg) * (-4 m/s) because it's moving in the opposite direction. So the total momentum before lunch is 5 kg⋅m/s + (-4 kg⋅m/s) = 1 kg⋅m/s.
Now, since momentum is conserved in an isolated system, the total momentum after lunch should also be 1 kg⋅m/s.
Since the 5 kg fish has swallowed the 1 kg fish, their velocities combine. Let's call the final velocity of the larger fish "vf". The equation for momentum after lunch is (5 kg + 1 kg) * vf = 1 kg⋅m/s.
Simplifying the equation, 6 kg * vf = 1 kg⋅m/s. Dividing both sides by 6 kg, we get vf = 1/6 m/s.
So, the speed of the larger fish after lunch is 1/6 m/s. I hope they both had a "fin"-tastic meal!
To find the speed of the larger fish after lunch, we can use the law of conservation of momentum. According to this law, the momentum before an event is equal to the momentum after the event.
The momentum of an object is given by the product of its mass and velocity (momentum = mass × velocity).
Let's denote the larger fish's mass as M and its velocity before eating as V. The smaller fish's mass is m, and its velocity is v.
The total momentum before lunch is the sum of the individual momenta:
Momentum before = (Mass of larger fish × Velocity of larger fish) + (Mass of smaller fish × Velocity of smaller fish)
P_before = (M × V) + (m × v)
After the larger fish swallows the smaller fish, their masses combine. The final mass of the larger fish is the sum of its original mass and the mass of the smaller fish. Therefore, the final mass is M + m.
The final velocity of the larger fish is denoted by V'.
According to the law of conservation of momentum, the momentum after lunch is equal to the momentum before:
P_after = (M + m) × V'
We can set the two equations equal to each other and solve for V':
(M × V) + (m × v) = (M + m) × V'
Now let's plug in the given values: M = 5 kg, V = 1 m/s, m = 1 kg, v = 4 m/s.
(5 × 1) + (1 × 4) = (5 + 1) × V'
5 + 4 = 6 × V'
9 = 6 × V'
Divide both sides by 6:
V' = 9/6
Simplifying, we have:
V' = 1.5 m/s
Therefore, the speed of the larger fish after lunch is 1.5 m/s.
To find the speed of the larger fish after lunch, we can apply the principle of conservation of momentum. According to this principle, the total momentum before and after an interaction remains constant, provided there are no external forces acting on the system.
The momentum (p) of an object can be calculated by multiplying its mass (m) by its velocity (v), using the equation: p = m * v.
Before the interaction, the momentum of the 5 kg fish is given by: p1 = m1 * v1 = 5 kg * 1 m/s = 5 kg m/s.
Similarly, the momentum of the 1 kg fish before the interaction is: p2 = m2 * v2 = 1 kg * (-4 m/s) = -4 kg m/s. (Here, the negative sign indicates that the fish is swimming in the opposite direction of the larger fish).
The total momentum before the interaction is the sum of these individual momenta: p_initial = p1 + p2 = 5 kg m/s - 4 kg m/s = 1 kg m/s.
Since there are no external forces acting on the system, the total momentum after the interaction will also be 1 kg m/s.
After the larger fish swallows the smaller fish, they combine to form a single system. Let's consider the mass of the combined system, denoted as M, and the velocity of the larger fish after lunch, denoted as V.
The momentum of the combined system after the interaction is given by: p_final = M * V.
Since the total momentum is conserved, we can equate the initial and final momentum: p_initial = p_final.
Therefore, 1 kg m/s = M * V.
The combined mass, M, of the fish is 5 kg (larger fish) + 1 kg (smaller fish) = 6 kg.
Plugging in the values, we can solve for V: 1 kg m/s = 6 kg * V.
V = 1 kg m/s / 6 kg = 1/6 m/s.
Hence, the speed of the larger fish after lunch is approximately 0.17 m/s.