A 300 g bird flying along at 6.4 m/s sees a 10 g insect heading straight toward it with a speed of 34 m/s (as measured by an observer on the ground, not by the bird). The bird opens its mouth wide and enjoys a nice lunch.
What is the bird's speed immediately after swallowing?
I cant figure this out!
Conservation of momentum:
mv+MV=(m+M)Vf
solve for Vf. Note that v, and V are opposite directions.
Awesome thanks a lot!
Well, it seems that the bird has decided to enjoy a satisfying snack! Now, let's figure out its speed after swallowing.
Since the bird has swallowed the insect, we can assume that its mass has increased by 10 g. So now the bird's mass is 310 g (300 g + 10 g).
However, the insect was moving at 34 m/s before the bird snatched it. When the bird gulped down the insect, it would have gained its momentum. This means the bird's speed would increase due to the insect's speed.
To calculate the bird's speed after swallowing, we need to apply the conservation of momentum principle. The total momentum before the snack should be equal to the total momentum after.
Since the bird is much larger than the insect, we can neglect any contribution from the bird's initial speed, assuming it was negligible. Therefore, we only need to consider the momentum of the insect before and after being eaten.
Before being eaten:
Momentum of insect = mass of insect × velocity of insect
= 10 g × 34 m/s
After being eaten:
Momentum of bird = mass of bird × velocity of bird after swallowing
= 310 g × velocity of bird after swallowing
Since momentum is conserved, we can equate the two:
10 g × 34 m/s = 310 g × velocity of bird after swallowing
Now we can solve for the velocity of the bird after swallowing:
velocity of bird after swallowing = (10 g × 34 m/s) / 310 g
Calculating this, we find that the bird's speed immediately after swallowing the insect is approximately 1.0968 m/s.
So, the bird can now happily fly away with a slightly increased speed!
To find the bird's speed immediately after swallowing the insect, we need to apply the law of conservation of momentum.
The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. In this case, we can consider the bird and the insect as a closed system.
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
Before swallowing the insect, the total momentum of the bird and the insect is given by the sum of their individual momenta:
Total momentum before = (mass of bird × velocity of bird) + (mass of insect × velocity of insect)
Let's calculate the total momentum before swallowing:
Total momentum before = (0.3 kg × 6.4 m/s) + (0.01 kg × 34 m/s)
= 1.92 kg·m/s + 0.34 kg·m/s
= 2.26 kg·m/s
According to the conservation of momentum, the total momentum after swallowing must also be 2.26 kg·m/s.
After swallowing the insect, the only mass that contributes to the bird's momentum is its own mass. So we can calculate the bird's speed immediately after swallowing using the equation:
Total momentum after = mass of bird × velocity after swallowing
Let's solve for the velocity after swallowing:
2.26 kg·m/s = 0.3 kg × velocity after swallowing
velocity after swallowing = 2.26 kg·m/s / 0.3 kg
= 7.53 m/s
Therefore, the bird's speed immediately after swallowing the insect is 7.53 m/s.