A great white shark with a mass of 3000 kg swimming at 3.00 m/s swallows a 250 kg fish at rest. What is the speed of the great white shark right after swallowing the fish?
2.5
To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event.
The momentum of an object is given by the product of its mass and velocity (p = mv).
Let's calculate the initial momentum of the great white shark before swallowing the fish:
Momentum of the shark = Mass of shark x Velocity of shark
= 3000 kg x 3.00 m/s
= 9000 kg·m/s
The initial momentum of the swallowed fish is zero since it is at rest.
Now, let's calculate the total momentum after the shark swallows the fish:
Momentum of the shark after swallowing = (Mass of shark + Mass of fish) x Velocity of the shark after swallowing
We know that the shark's mass is 3000 kg, and the mass of the fish is 250 kg.
Momentum of the shark after swallowing = (3000 kg + 250 kg) x Velocity of the shark after swallowing
Let's call the velocity of the shark after swallowing "v".
Momentum of the shark after swallowing = 3250 kg x v
According to the principle of conservation of momentum, the total momentum before and after the event should be equal:
9000 kg·m/s = 3250 kg x v
Now, let's solve for "v":
v = 9000 kg·m/s / 3250 kg
v ≈ 2.769 m/s
Therefore, the speed of the great white shark right after swallowing the fish is approximately 2.769 m/s.
To determine the speed of the great white shark right after swallowing the fish, we can apply the principle of conservation of momentum. According to this principle, the total momentum before and after the event should remain the same.
Before the shark swallows the fish, the total momentum is given by the equation:
Total momentum before = (Mass of the shark) x (Velocity of the shark)
After the fish is swallowed, the total momentum is:
Total momentum after = (Mass of the shark + Mass of the fish) x (Velocity of the shark after)
Since momentum is conserved, the total momentum before must equal the total momentum after. Therefore, we can set up the equation:
(Mass of the shark) x (Velocity of the shark) = (Mass of the shark + Mass of the fish) x (Velocity of the shark after)
Let's plug in the given values:
Mass of the shark = 3000 kg
Velocity of the shark = 3.00 m/s
Mass of the fish = 250 kg
3000 kg x 3.00 m/s = (3000 kg + 250 kg) x (Velocity of the shark after)
9000 kg·m/s = 3250 kg x (Velocity of the shark after)
To solve for the velocity of the shark after swallowing the fish, we'll rearrange the equation:
Velocity of the shark after = (9000 kg·m/s) / (3250 kg)
Velocity of the shark after = 2.77 m/s
Therefore, the speed of the great white shark right after swallowing the fish is approximately 2.77 m/s.