A 2.70 kg bird is flying past a tree that has a 4.60 kg chipmunk in it. The chipmunk decides to jump on the bird so he can fly too. As the bird is flying past the tree, the chipmunk leaps off at 8.90 m/s in the same direction the bird is flying and lands on the bird. Immediately after the collision, the bird and chipmunk together have a speed of 11.6 m/s. What was the initial speed of the bird? 15.2 m/s 31.4 m/s 16.2 m/s 5.99 m/s
Question
A 2.70 kg bird is flying past a tree that has a 4.60 kg chipmunk in it. The chipmunk decides to jump on the bird so he can fly too. As the bird is flying past the tree, the chipmunk leaps off at 8.90 m/s in the same direction the bird is flying and lands on the bird. Immediately after the collision, the bird and chipmunk together have a speed of 11.6 m/s. What was the initial speed of the bird? 15.2 m/s 31.4 m/s 16.2 m/s 5.99 m/s
Solution
This problem can be solved using the principle of conservation of momentum. The total momentum before the collision (chipmunk jumping on the bird) is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and its velocity (p = mv).
Before the collision, the bird is flying with a velocity we need to find (let's call it v), and the chipmunk is jumping off the tree with a velocity of 8.90 m/s.
So, the total momentum before the collision is:
P_before = (mass of bird * velocity of bird) + (mass of chipmunk * velocity of chipmunk) P_before = (2.70 kg * v) + (4.60 kg * 8.90 m/s)
After the collision, the bird and chipmunk are moving together with a velocity of 11.6 m/s.
So, the total momentum after the collision is:
P_after = (mass of bird + mass of chipmunk) * velocity after collision P_after = (2.70 kg + 4.60 kg) * 11.6 m/s
According to the principle of conservation of momentum, P_before = P_after.
So, we can set up the equation and solve for v:
(2.70 kg * v) + (4.60 kg * 8.90 m/s) = (2.70 kg + 4.60 kg) * 11.6 m/s
Solving this equation will give us the initial speed of the bird.
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