You are analyzing the possible defenses for an asteroid that is going to crash into Earth.Initially, the asteroid of mass ma is traveling to the left with speed vai . A missile of mass mm with initial velocity vmi to the right collides with the asteroid, and embeds itself inside the asteroid. Find the common final velocity of the missile and asteroid after the collision.ma = 1.3000E+9 kgmm = 9.1000E+7 kgvai x = -2200 m/svmi x = 12571 m/s[the final velocity for this one was -1233.67m/s] = vf xThe missile then explodes, causing the asteroid to break into two chunks of mass m1 and m2. Solve algebraically for the final speeds of pieces 1 and 2 in terms of the masses of the two pieces (m1 and m2), the angles, the total mass before the explosion, and vf x (the velocity after the collision that you found above).Then use the following values for the parameters to get values for the speeds:m1 = 2.7820E+8 kgm2 = 1.1128E+9 kgθ1 = 30.2 degreesθ2 = 52.5 degreesThis problem is dealing with impulse and this second part is an inelastic collision. We are supposed to solve for v1f and v2f, but I don't know how we are supposed to solve for two unknowns at the same time. I know that momentum is conserved for the whole system of both pieces, but I can't figure out how to find the velocities from that. The image is a diagram showing a missile approaching a cloud or target area. The vector \( \vec{V}_{mi} \) represents the initial velocity vector of the missile, while the vector \( \vec{V}_{ai} \) represents the initial velocity vector of the air or target. Both vectors are pointing towards each other, indicating opposite directions. This can illustrate concepts such as relative motion, vector analysis, or collision courses in physics and engineering contexts.- \( \vec{V}_{mi} \): Initial velocity vector of the missile.- \( \vec{V}_{ai} \): Initial velocity vector of the air or target.The dashed line between the two vectors signifies the path or line of interaction, which can be used to analyze relative velocities or interception trajectories. The image presents a diagram illustrating the scattering process between two objects labeled as "1" and "2". Key elements are:1. **Objects and Arrows**: - Object "1" is shown at the top left. - Object "2" is located at the bottom right. - The arrows labeled \(\vec{v_1}\) and \(\vec{v_2}\) indicate the velocity vectors of objects "1" and "2", respectively.2. **Dashed Line and Angles**: - A dashed line connects the two objects, representing the initial path or interaction line. - Two angles are marked: - \(\theta_1\) is the angle between the dashed line and \(\vec{v_1}\). - \(\theta_2\) is the angle between the dashed line and \(\vec{v_2}\).3. **Axes**: - The horizontal and vertical lines indicate a reference axis for illustrating motion or vector directions.This diagram is typically used in physics to explain concepts such as collision angles, momentum, and directionality in scattering experiments or mechanics problems.

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You are analyzing the possible defenses for an asteroid that is going to crash into Earth. Initially, the asteroid of mass ma is traveling to the left with speed vai . A missile of mass mm with initial velocity vmi to the right collides with the asteroid, and embeds itself inside the asteroid. Find the common final velocity of the missile and asteroid after the collision. ma = 1.3000E+9 kg mm = 9.1000E+7 kg vai x = -2200 m/s vmi x = 12571 m/s [the final velocity for this one was -1233.67m/s] = vf x The missile then explodes, causing the asteroid to break into two chunks of mass m1 and m2. Solve algebraically for the final speeds of pieces 1 and 2 in terms of the masses of the two pieces (m1 and m2), the angles, the total mass before the explosion, and vf x (the velocity after the collision that you found above). Then use the following values for the parameters to get values for the speeds: m1 = 2.7820E+8 kg m2 = 1.1128E+9 kg θ1 = 30.2 degrees θ2 = 52.5 degrees This problem is dealing with impulse and this second part is an inelastic collision. We are supposed to solve for v1f and v2f, but I don't know how we are supposed to solve for two unknowns at the same time. I know that momentum is conserved for the whole system of both pieces, but I can't figure out how to find the velocities from that.

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You are analyzing the possible defenses for an asteroid that is going to crash into Earth.
Initially, the asteroid of mass m_a is traveling to the left with speed v_ai . A missile of mass m_m with initial velocity v_mi to the right collides with the asteroid, and embeds itself inside the asteroid. Find the common final velocity of the missile and asteroid after the collision.

m_a= 1.3000E+9 kg
m_m = 9.1000E+7 kg
v_ai x = -2200 m/s
v_mi x = 12571 m/s

[the final velocity for this one was -1233.67m/s] = v_{f x}

The missile then explodes, causing the asteroid to break into two chunks of mass m₁ and m₂. Solve algebraically for the final speeds of pieces 1 and 2 in terms of the masses of the two pieces (m₁ and m₂), the angles, the total mass before the explosion, and v_{f x} (the velocity after the collision that you found above).

Then use the following values for the parameters to get values for the speeds:

m₁ = 2.7820E+8 kg
m₂ = 1.1128E+9 kg
θ₁ = 30.2 degrees
θ₂ = 52.5 degrees

This problem is dealing with impulse and this second part is an inelastic collision. We are supposed to solve for v_1f and v_2f, but I don't know how we are supposed to solve for two unknowns at the same time. I know that momentum is conserved for the whole system of both pieces, but I can't figure out how to find the velocities from that.

The image is a diagram showing a missile approaching a cloud or target area. The vector \( \vec{V}_{mi} \) represents the initial velocity vector of the missile, while the vector \( \vec{V}_{ai} \) represents the initial velocity vector of the air or target. Both vectors are pointing towards each other, indicating opposite directions. This can illustrate concepts such as relative motion, vector analysis, or collision courses in physics and engineering contexts.

- \( \vec{V}_{mi} \): Initial velocity vector of the missile.
- \( \vec{V}_{ai} \): Initial velocity vector of the air or target.

The dashed line between the two vectors signifies the path or line of interaction, which can be used to analyze relative velocities or interception trajectories.

The image presents a diagram illustrating the scattering process between two objects labeled as "1" and "2".

Key elements are:

1. **Objects and Arrows**:
- Object "1" is shown at the top left.
- Object "2" is located at the bottom right.
- The arrows labeled \(\vec{v_1}\) and \(\vec{v_2}\) indicate the velocity vectors of objects "1" and "2", respectively.

2. **Dashed Line and Angles**:
- A dashed line connects the two objects, representing the initial path or interaction line.
- Two angles are marked:
- \(\theta_1\) is the angle between the dashed line and \(\vec{v_1}\).
- \(\theta_2\) is the angle between the dashed line and \(\vec{v_2}\).

3. **Axes**:
- The horizontal and vertical lines indicate a reference axis for illustrating motion or vector directions.

This diagram is typically used in physics to explain concepts such as collision angles, momentum, and directionality in scattering experiments or mechanics problems.

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