Two birds of prey hurtling after the same mouse collide in mid-air and grab each other with their talons. Each 250-g bird is flying at 30 m/s at a 60° angle to the ground.

Use this exhibit to answer the following question(s).
-What is the magnitude of their total momentum, in , immediately after the collision?
A)0
B)6.5
C)7.5
D)13
E)15

Question

Two birds of prey hurtling after the same mouse collide in mid-air and grab each other with their talons. Each 250-g bird is flying at 30 m/s at a 60° angle to the ground.
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Use this exhibit to answer the following question(s).
-What is the magnitude of their total momentum, in  , immediately after the collision?
A)0 
B)6.5 
C)7.5 
D)13 
E)15

Quizplus · Accepted Answer

Since the birds collide and grab each other, they will move together as one system after the collision. Therefore, their total momentum immediately after the collision is equal to the sum of their individual momenta before the collision.

To calculate their individual momenta before the collision, we need to use vector addition.

For Bird 1: 
Magnitude of momentum = 0.25 kg x 30 m/s = 7.5 kg m/s at a 60° angle to the ground, which can be resolved into horizontal and vertical components: 
Horizontal momentum = 7.5 kg m/s x cos(60°) = 3.75 kg m/s
Vertical momentum = 7.5 kg m/s x sin(60°) = 6.49 kg m/s

For Bird 2: 
Magnitude of momentum = 0.25 kg x 30 m/s = 7.5 kg m/s at a 120° angle to the ground, which can be resolved into horizontal and vertical components: 
Horizontal momentum = 7.5 kg m/s x cos(120°) = -3.75 kg m/s (opposite direction to Bird 1's horizontal momentum)
Vertical momentum = 7.5 kg m/s x sin(120°) = 6.49 kg m/s

When the birds collide, their horizontal momenta cancel out each other (since they are in opposite directions), and their vertical momenta add up: 
Total momentum = 3.75 kg m/s + (-3.75 kg m/s) = 0 kg m/s (horizontal)
Total momentum = 6.49 kg m/s + 6.49 kg m/s = 12.98 kg m/s (vertical)

Using the Pythagorean theorem, we can find the magnitude of their total momentum: 
Total momentum = sqrt((0 kg m/s)^2 + (12.98 kg m/s)^2) = 13 kg m/s

Therefore, the correct answer is (D) 13.

Two Birds of Prey Hurtling After the Same Mouse Collide