A 18kg fish moving horizontally to the right at 3.2m/s swallows a 2kg fish that is swimming to the left at 7.4m/s. What is the speed of the forces exerted on the pitches by the water is neiligible
We can disregard the forces exerted by the water, as they will be negligible. To find the final speed of the two fish after the collision, we'll apply the conservation of momentum principle. The total momentum before the collision (momentum_1) will be equal to the total momentum after the collision (momentum_2).
momentum_1 = momentum_2
In this case, momentum is the mass of the fish multiplied by its velocity. The velocity of the fish is given in m/s:
momentum_1 = 18 kg * 3.2 m/s - 2 kg * 7.4 m/s
momentum_1 = 57.6 kg*m/s - 14.8 kg*m/s
momentum_1 = 42.8 kg*m/s
When the fish collide, they will move together at a new velocity (V), and their combined mass will be 20 kg since the smaller fish has a mass of 2 kg and the larger fish has a mass of 18 kg.
momentum_2 = (18 kg + 2 kg) * V
momentum_2 = 20 kg * V
Now we can equate momentums and solve for the new velocity (V):
42.8 kg*m/s = 20 kg * V
V = 42.8 kg*m/s / 20 kg
V = 2.14 m/s
After the collision, the fish will move together with a velocity of 2.14 m/s to the right.
To find the speed of the forces exerted on the fishes, we first need to understand the concept of momentum conservation. The law of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, assuming no external forces act on the system.
Let's denote the initial momentum of the 18 kg fish moving to the right as P₁ and the initial momentum of the 2 kg fish swimming to the left as P₂.
P₁ = mass₁ * velocity₁ = 18 kg * 3.2 m/s = 57.6 kg·m/s
P₂ = mass₂ * velocity₂ = 2 kg * (-7.4 m/s) = -14.8 kg·m/s
Using the principle of momentum conservation, we can set up the equation:
P₁ + P₂ = P
Where P is the total momentum after the event.
57.6 kg·m/s + (-14.8 kg·m/s) = P
Simplifying the equation gives:
42.8 kg·m/s = P
Since momentum is a vector quantity, the total momentum after the event is equal to the sum of the momenta of each individual fish.
Now, let's denote the final velocity of the combined system (both fishes) as V.
P = (mass₁ + mass₂) * V
42.8 kg·m/s = (18 kg + 2 kg) * V
42.8 kg·m/s = 20 kg * V
Divide both sides by 20 kg:
42.8 kg·m/s / 20 kg = V
V ≈ 2.14 m/s
Therefore, the speed of the forces exerted on the fishes is approximately 2.14 m/s.