A 15kg tuna fish moving horizontally to the right at 5m/s swallows a 2kg fish that is swimming to the left at 7.5 m/s .What is the speed of the tuna fish immediately after,if the force exerted on the fish by the water can be neglected?
To solve this problem, we can use the law of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Before the collision, the momentum of the tuna fish (mass = 15 kg) can be calculated using the formula:
Momentum of tuna fish = mass * velocity
Momentum of tuna fish = 15 kg * 5 m/s
Momentum of tuna fish = 75 kg·m/s
Before the collision, the momentum of the smaller fish (mass = 2 kg) can be calculated using the formula:
Momentum of smaller fish = mass * velocity
Momentum of smaller fish = 2 kg * (-7.5 m/s) (Note that the velocity is negative because it is moving to the left.)
Momentum of smaller fish = -15 kg·m/s
Now, let's find the total momentum before the collision:
Total momentum before = momentum of tuna fish + momentum of smaller fish
Total momentum before = 75 kg·m/s + (-15 kg·m/s)
Total momentum before = 60 kg·m/s
According to the conservation of momentum principle, the total momentum after the collision is the same as the total momentum before the collision:
Total momentum after = 60 kg·m/s
After the collision, the tuna fish will be moving with a new velocity (let's call it V). To find V, we need to determine the mass of the combined fish.
After the tuna fish swallows the smaller fish, the new mass of the combined fish will be the sum of their masses:
New mass = mass of tuna fish + mass of smaller fish
New mass = 15 kg + 2 kg
New mass = 17 kg
Now we can find the velocity (V) of the combined fish after the collision using the formula:
Total momentum after = new mass * V
60 kg·m/s = 17 kg * V
Divide both sides of the equation by 17 kg:
V = 60 kg·m/s / 17 kg
V ≈ 3.53 m/s
Therefore, the speed of the tuna fish immediately after swallowing the smaller fish is approximately 3.53 m/s in the rightward direction.
To solve this problem, we can use the principle of conservation of linear momentum. According to this principle, the total momentum before the interaction is equal to the total momentum after the interaction, assuming no external forces are acting on the system.
The momentum (p) of an object is defined as the product of its mass (m) and velocity (v): p = m * v.
Let's calculate the total momentum before the interaction:
For the 15kg tuna fish:
Momentum (p1) = mass (m1) * velocity (v1) = 15kg * 5m/s = 75 kg*m/s (to the right)
For the 2kg fish:
Momentum (p2) = mass (m2) * velocity (v2) = 2kg * (-7.5m/s) = -15 kg*m/s (to the left)
Since the direction of momentum is important, we give the leftward momentum a negative sign.
Now, let's consider the total momentum after the interaction:
The 15kg tuna fish has swallowed the 2kg fish, so they move together with a single velocity (let's call it v3). The combined mass of the fish is 15kg + 2kg = 17kg.
Total momentum after the interaction (p3) = mass (m3) * velocity (v3) = 17kg * v3
According to the conservation of linear momentum, the total momentum before the interaction (p1 + p2) is equal to the total momentum after the interaction (p3):
p1 + p2 = p3
75 kg*m/s + (-15 kg*m/s) = 17kg * v3
60 kg*m/s = 17kg * v3
To find the velocity (v3), we divide both sides of the equation by 17kg:
v3 = (60 kg*m/s) / 17kg
v3 ≈ 3.53 m/s
Therefore, the speed of the tuna fish immediately after swallowing the other fish is approximately 3.53 m/s to the right.
conserve momentum
15(5) + 2(7.5) = 17v
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