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2-D Collision and Explosion You are analyzing the possible defenses for an asteroid that is going to crash into Earth. Initially, the asteroid of mass m, is traveling to the left with speed v. A missile of mass mm with initial velocity v to the right collides with the asteroid, and embeds itself inside the asteroid. See the figure below. Vmi V ai Find the common final velocity of the missile and asteroid after the collision. Use an x axis with positive pointing to the right. Solve algebraically first, then use the following values for the parameters to get a value for v: m, = 2.3000E+9 kg Mm = 9.2000E+7 kg Vix -1800 m/s mix = 16200 m/s Vi = -1.10769x103 m/s 1pts You are correct. Your receipt no. is 165-1609 e PreviOus Tries

2-D Collision and Explosion You are analyzing the possible defenses for an asteroid that is going to crash into Earth. Initially, the asteroid of mass m, is traveling to the left with speed v. A missile of mass mm with initial velocity v to the right collides with the asteroid, and embeds itself inside the asteroid. See the figure below. Vmi V ai Find the common final velocity of the missile and asteroid after the collision. Use an x axis with positive pointing to the right. Solve algebraically first, then use the following values for the parameters to get a value for v: m, = 2.3000E+9 kg Mm = 9.2000E+7 kg Vix -1800 m/s mix = 16200 m/s Vi = -1.10769x103 m/s 1pts You are correct. Your receipt no. is 165-1609 e PreviOus Tries

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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The missile then explodes, causing the asteroid to break into two chunks of mass \( m_1 \) and \( m_2 \). ![Diagram of Explosion](Diagram of Explosion show chunks of mass \( m_1 \) and \( m_2 \) with angles \( \theta_1 \) and \( \theta_2 \) and velocities \( \vec{v}_1 \) and \( \vec{v}_2 \). **Solve algebraically for the final speeds of pieces 1 and 2 in terms of the masses of the two pieces (\( m_1 \) and \( m_2 \)), the angles, the total mass before the explosion, and \( v_x \) (the velocity after the collision that you found above).** Then use the following values for the parameters to get values for the speeds: - \( m_1 = 1.4352E+9 \) kg - \( m_2 = 9.6580E+8 \) kg - \( \theta_2 = 27.1 \) degrees - \( \theta_1 = 63.7 \) degrees
Transcribed Image Text:The missile then explodes, causing the asteroid to break into two chunks of mass \( m_1 \) and \( m_2 \). ![Diagram of Explosion](Diagram of Explosion show chunks of mass \( m_1 \) and \( m_2 \) with angles \( \theta_1 \) and \( \theta_2 \) and velocities \( \vec{v}_1 \) and \( \vec{v}_2 \). **Solve algebraically for the final speeds of pieces 1 and 2 in terms of the masses of the two pieces (\( m_1 \) and \( m_2 \)), the angles, the total mass before the explosion, and \( v_x \) (the velocity after the collision that you found above).** Then use the following values for the parameters to get values for the speeds: - \( m_1 = 1.4352E+9 \) kg - \( m_2 = 9.6580E+8 \) kg - \( \theta_2 = 27.1 \) degrees - \( \theta_1 = 63.7 \) degrees
# 2-D Collision and Explosion ## Problem Overview You are analyzing the possible defenses for an asteroid that is heading towards Earth. Initially, the asteroid with mass \( m_a \) is traveling to the left with speed \( v_{ai} \). A missile with mass \( m_m \) and an initial velocity \( v_{mi} \) to the right collides with the asteroid and becomes embedded inside it. ### Objective Find the common final velocity of the missile and asteroid after the collision. ### Coordinate System Use an x-axis with the positive direction pointing to the right. ### Instructions Solve algebraically first, then use the given values to calculate \( v_{f_x} \). ### Given Data - Mass of asteroid, \( m_a = 2.3000 \times 10^9 \) kg - Mass of missile, \( m_m = 9.2000 \times 10^7 \) kg - Initial velocity of asteroid, \( v_{ai} = -1800 \) m/s - Initial velocity of missile, \( v_{mi} = 16200 \) m/s ### Calculation Using the principle of conservation of momentum: \[ v_{f_x} = \frac{m_m \cdot v_{mi} + m_a \cdot v_{ai}}{m_m + m_a} \] ### Result The calculated final velocity \( v_{f_x} \) is \(-1.10769 \times 10^3\) m/s. **Note:** You are correct. Your receipt no. is 165-1609. ## Diagram Explanation The diagram illustrates a missile moving to the right with velocity \( \vec{v}_{mi} \) and an asteroid moving to the left with velocity \( \vec{v}_{ai} \). The collision is depicted at the point where the missile embeds itself into the asteroid. Both objects are shown in simplified shapes with direction vectors indicating their velocities.
Transcribed Image Text:# 2-D Collision and Explosion ## Problem Overview You are analyzing the possible defenses for an asteroid that is heading towards Earth. Initially, the asteroid with mass \( m_a \) is traveling to the left with speed \( v_{ai} \). A missile with mass \( m_m \) and an initial velocity \( v_{mi} \) to the right collides with the asteroid and becomes embedded inside it. ### Objective Find the common final velocity of the missile and asteroid after the collision. ### Coordinate System Use an x-axis with the positive direction pointing to the right. ### Instructions Solve algebraically first, then use the given values to calculate \( v_{f_x} \). ### Given Data - Mass of asteroid, \( m_a = 2.3000 \times 10^9 \) kg - Mass of missile, \( m_m = 9.2000 \times 10^7 \) kg - Initial velocity of asteroid, \( v_{ai} = -1800 \) m/s - Initial velocity of missile, \( v_{mi} = 16200 \) m/s ### Calculation Using the principle of conservation of momentum: \[ v_{f_x} = \frac{m_m \cdot v_{mi} + m_a \cdot v_{ai}}{m_m + m_a} \] ### Result The calculated final velocity \( v_{f_x} \) is \(-1.10769 \times 10^3\) m/s. **Note:** You are correct. Your receipt no. is 165-1609. ## Diagram Explanation The diagram illustrates a missile moving to the right with velocity \( \vec{v}_{mi} \) and an asteroid moving to the left with velocity \( \vec{v}_{ai} \). The collision is depicted at the point where the missile embeds itself into the asteroid. Both objects are shown in simplified shapes with direction vectors indicating their velocities.
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