A 1.00-kg duck is flying overhead at 1.50 m/s when a hunter fires straight up. The 0.010 0-kg bullet is moving 100 m/s when it hits the duck and stays lodged in the duck's body. What is the speed of the duck and bullet immediately after the hit?
m1= 1kg
v1= 1.50 m/s
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m2= 0.010kg
v2= 100m/s
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m1*v1= 1kg*1.50kg= 1.50kg-m/s
m2*v2= 0.010kg*100m/s= 1.0kg-m/s
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mTotal= 1.010kg
Since the bullet is shot in a vertical movement, and the duck was flying horizontally, then we can use Pythagorean to solve for the final velocity(vF).
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Velocity in the x-component(vx)
-> (mT)(vx)= momentum of duck.
--> (1.010kg((vx)= 1.50kg-m/s
---> (vx)= (1.50kg-m/s)/(1.010kg-m/s)
----> (vx)= 1.485m/s
....
Velocity in the y-component (vy)
-> (mT)(vy)= 1.0kg-m/s
--> (1.010kg)(vy)= (1.0kg-m/s)
---> (vy)= (1.0kg-m/s)/(1.010kg-m/s)
----> (vy)= (0.99009m/s)
=====
*Now we can use Pythagorean to solve for the final velocity!
-> a^2 + b^2 = c^2
--> (1.485m/s)^2 + (0.99009m/s)^2 = c^2
---> 2.2055m/s + 0.9818m/s = c^2
----> 3.1871m/s = c^2
-----> c = √(3.1871m/s)
------> c = 1.785 m/s!
* Your final velocity is 1.785m/s!
Well, that's definitely a "quack"tastic situation! Let's calculate the final speed of the duck and bullet after the hit, shall we?
To solve this, we can use the principle of conservation of momentum. The initial momentum of the duck and bullet before the hit is equal to the final momentum after the hit:
Initial momentum = Final momentum
The initial momentum is given by the product of the mass and velocity of the duck:
Initial momentum = (mass of duck) x (velocity of duck)
Final momentum is given by the sum of the mass and velocity of the bullet and the mass and velocity of the duck (with the bullet now lodged in the duck):
Final momentum = (mass of bullet + mass of duck) x (final velocity)
Let's plug in the values:
Initial momentum = (1.00 kg) x (1.50 m/s) = 1.50 kg m/s
Final momentum = (0.010 kg + 1.00 kg) x (final velocity)
Since the bullet stays lodged in the duck, the final velocity of both the duck and the bullet is the same. Let's call it V.
Final momentum = (1.010 kg) x (V)
Now, equating the initial and final momenta:
1.50 kg m/s = (1.010 kg) x (V)
Solving for V:
V = 1.50 kg m/s / 1.010 kg
V ≈ 1.48 m/s
So, the speed of the duck and bullet immediately after the hit is approximately 1.48 m/s.
Looks like the duck got a "bulletproof" makeover!
To find the speed of the duck and bullet immediately after the hit, we can use the law of conservation of momentum.
According to the law of conservation of momentum, the total momentum before the hit must be equal to the total momentum after the hit. Momentum is defined as the product of an object's mass and its velocity.
Before the hit, the momentum of the duck is given by:
Momentum of duck before = mass of duck × velocity of duck = (1.00 kg) × (1.50 m/s) = 1.50 kg·m/s
The momentum of the bullet before the hit is given by:
Momentum of bullet before = mass of bullet × velocity of bullet = (0.010 kg) × (100 m/s) = 1.00 kg·m/s
The total momentum before the hit is the sum of the momenta of the duck and the bullet:
Total momentum before = Momentum of duck before + Momentum of bullet before = 1.50 kg·m/s + 1.00 kg·m/s = 2.50 kg·m/s
According to the law of conservation of momentum, the total momentum after the hit must also be 2.50 kg·m/s.
Since the bullet becomes lodged in the duck's body, their velocities after the hit will be the same. Let's assume their combined speed after the hit is v.
The momentum of the duck and bullet after the hit is given by:
Total momentum after = (mass of duck + mass of bullet) × velocity after
Since the bullet is lodged in the duck's body, the mass of the duck and bullet combined is:
Mass of duck and bullet after = Mass of duck + Mass of bullet = 1.00 kg + 0.010 kg = 1.01 kg
Therefore, the momentum of the duck and bullet after the hit is:
Total momentum after = (1.01 kg) × v
According to the law of conservation of momentum, the total momentum before the hit must equal the total momentum after the hit. Therefore, we can set up the following equation:
Total momentum before = Total momentum after
2.50 kg·m/s = (1.01 kg) × v
Solving for v, we get:
v = (2.50 kg·m/s) / (1.01 kg) ≈ 2.48 m/s
Therefore, the speed of the duck and bullet immediately after the hit is approximately 2.48 m/s.
To find the speed of the duck and bullet immediately after the hit, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the hit should be equal to the total momentum after the hit.
The momentum of an object is given by its mass multiplied by its velocity. Therefore, the momentum of the duck before the hit would be (mass of duck) x (velocity of duck), and the momentum of the bullet before the hit would be (mass of bullet) x (velocity of bullet).
Let's calculate the initial momentum of the duck and bullet:
Momentum of the duck before the hit = (mass of duck) x (velocity of duck)
= (1.00 kg) x (1.50 m/s)
= 1.50 kg m/s
Momentum of the bullet before the hit = (mass of bullet) x (velocity of bullet)
= (0.010 kg) x (100 m/s)
= 1.00 kg m/s
Now, since the bullet stays lodged in the duck's body and they move together after the hit, the total mass after the hit would be the sum of the masses of the duck and bullet, and the total momentum after the hit would be the sum of their individual momenta.
Total mass after the hit = (mass of duck) + (mass of bullet)
= (1.00 kg) + (0.010 kg)
= 1.01 kg
Total momentum after the hit = Total momentum before the hit
Now, we can solve for the velocity of the duck and bullet after the hit using the equation:
Total momentum after the hit = (total mass after the hit) x (final velocity)
Substituting the values, we have:
(1.50 kg m/s) + (1.00 kg m/s) = (1.01 kg) x (final velocity)
Simplifying the equation:
2.50 kg m/s = 1.01 kg x (final velocity)
Now, divide both sides of the equation by 1.01 kg:
(final velocity) = (2.50 kg m/s) / (1.01 kg)
≈ 2.48 m/s
Therefore, the speed of the duck and bullet immediately after the hit is approximately 2.48 m/s.