A 0.205 kg bird flying along at 7.8 m/s sees a 0.029 kg insect heading straight toward it with a speed of 15 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 the insect?
M1*V1 + M2*V2 = M1*V + M2*V
0.205*7.8 + 0.029*15 = 0.205*V + 0.029*V
Solve for V.
To find the bird's speed immediately after swallowing the insect, we can use the principle of conservation of momentum, which states that the total momentum before an event is equal to the total momentum after the event. In this case, the momentum of the bird before swallowing the insect should be equal to the momentum of the bird after swallowing the insect.
Before swallowing the insect, the momentum of the bird is given by:
Momentum of bird before = mass of bird * velocity of bird = (0.205 kg) * (7.8 m/s)
After swallowing the insect, the momentum of the bird will be the sum of the momenta of the bird and the insect. Since the bird consumes the insect, the combined mass will be the mass of the bird and the insect:
Mass of bird after swallowing = mass of bird + mass of insect = 0.205 kg + 0.029 kg
Now we can calculate the momentum of the bird after swallowing the insect:
Momentum of bird after = mass of bird after * velocity of bird after
We are trying to find the velocity of bird after, so we can rearrange the equation:
Velocity of bird after = Momentum of bird after / mass of bird after
Plugging in the values:
Velocity of bird after = (Momentum of bird before) / (mass of bird + mass of insect)
Calculating the momentum of the bird before:
Momentum of bird before = (0.205 kg) * (7.8 m/s)
Calculating the total mass of the bird and the insect:
Mass of bird after = 0.205 kg + 0.029 kg
Finally, we can calculate the velocity of the bird after swallowing the insect by dividing the momentum of the bird before by the mass of the bird after:
Velocity of bird after = (0.205 kg * 7.8 m/s) / (0.205 kg + 0.029 kg)