A 3.8 kg fish swimming 1.3 m/s swallows an absent minded 1.4 kg fish swimming toward it at a velocity that brings both fish to a halt immediately after lunch. What is the velocity v of the smaller fish before lunch?
The momenta of the two fish before "lunch" must be equal and opposite in order for the final momenum fo be zero. If v is the unknown velocity,
3.8*1.3 + 1.4*v = 0
v = -(3.8*1.3)/1.4 = __
-3.52857
To solve this problem, we can apply the law of conservation of momentum. According to this law, the total momentum before the interaction should be equal to the total momentum after the interaction.
Let's assume that the velocity of the smaller fish before lunch is v.
The momentum of an object can be calculated by multiplying its mass by its velocity. Using this information, we can write the following equation:
(3.8 kg) * (1.3 m/s) + (1.4 kg) * v = 0
This equation represents the total momentum before the interaction, which should be equal to zero after the interaction resulting in both fish coming to a halt.
Now, let's solve for v:
3.8 * 1.3 + 1.4 * v = 0
4.94 + 1.4v = 0
1.4v = -4.94
v = -4.94 / 1.4
v ≈ -3.53 m/s
Therefore, the velocity of the smaller fish before lunch is approximately -3.53 m/s. Note that the negative sign indicates that the fish was moving in the opposite direction to the larger fish.
To find the velocity of the smaller fish before lunch, we can use the law of conservation of momentum. According to this law, the total momentum before an event is equal to the total momentum after the event.
Mathematically, we can express momentum as:
Momentum (p) = mass (m) * velocity (v)
Where:
- Momentum is measured in kg⋅m/s
- Mass is measured in kg
- Velocity is measured in m/s
Let's denote the smaller fish's velocity before lunch as v1 and the larger fish's velocity before lunch as v2.
We know the following information:
- The mass of the larger fish (m2) = 3.8 kg
- The velocity of the larger fish (v2) = 1.3 m/s
- The mass of the smaller fish (m1) = 1.4 kg
- The final velocity of both fish after lunch (vf) = 0 m/s
According to the conservation of momentum, the total momentum before lunch (m1 * v1 + m2 * v2) should be equal to the total momentum after lunch (0, as the fish come to a halt):
m1 * v1 + m2 * v2 = 0
Now we can substitute the known values:
(1.4 kg) * v1 + (3.8 kg) * (1.3 m/s) = 0
Rearranging the equation to solve for v1:
(1.4 kg) * v1 = -(3.8 kg) * (1.3 m/s)
v1 = -((3.8 kg) * (1.3 m/s)) / (1.4 kg)
Simplifying the expression:
v1 = -3.514 m/s
Therefore, the velocity (v) of the smaller fish before lunch is approximately -3.514 m/s. The negative sign suggests that the smaller fish was swimming in the opposite direction of the larger fish before lunch.