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4 Problem Captain Jean-Luc Picard decides, as a last resort, to ram the asteroid (of mass mg = 2,000 kg) with his starship (of mass mA = 1,000 kg) in an attempt to deflect it from the planet. At the instant just before Capt. Picard decides to take action the Enterprise and the asteroid are moving in opposite directions, at speeds VA = 300 m/s and VB = 500 m/s, respectively. Part A: Capt. Picard commands his helmsman, Geordi La Forge, to match the asteroids speed and intercept it at an angle 0 = 60 deg.. Geordi sets the thruster to apply an impulse of At = 2 seconds but is unsure what directions the thrusters should point and how much force they should apply. What is the average force vector that Geordi must command during this interval? Part B: After the impulse, the Enterprise becomes embedded in the asteroid. What is their combined speed and direction? Before After A Impact 0 UB VA Impact

4 Problem Captain Jean-Luc Picard decides, as a last resort, to ram the asteroid (of mass mg = 2,000 kg) with his starship (of mass mA = 1,000 kg) in an attempt to deflect it from the planet. At the instant just before Capt. Picard decides to take action the Enterprise and the asteroid are moving in opposite directions, at speeds VA = 300 m/s and VB = 500 m/s, respectively. Part A: Capt. Picard commands his helmsman, Geordi La Forge, to match the asteroids speed and intercept it at an angle 0 = 60 deg.. Geordi sets the thruster to apply an impulse of At = 2 seconds but is unsure what directions the thrusters should point and how much force they should apply. What is the average force vector that Geordi must command during this interval? Part B: After the impulse, the Enterprise becomes embedded in the asteroid. What is their combined speed and direction? Before After A Impact 0 UB VA Impact

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# Problem Captain Jean-Luc Picard decides, as a last resort, to ram the asteroid (of mass \( m_B = 2,000 \, \text{kg} \)) with his starship (of mass \( m_A = 1,000 \, \text{kg} \)) in an attempt to deflect it from the planet. At the instant just before Capt. Picard decides to take action, the Enterprise and the asteroid are moving in opposite directions, at speeds \( v_A = 300 \, \text{m/s} \) and \( v_B = 500 \, \text{m/s} \), respectively. ### Part A: Capt. Picard commands his helmsman, Geordi La Forge, to match the asteroid's speed and intercept it at an angle \( \theta = 60 \, \text{deg.} \). Geordi sets the thruster to apply an impulse of \( \Delta t = 2 \) seconds but is unsure what direction the thrusters should point and how much force they should apply. What is the average force vector that Geordi must command during this interval? ### Part B: After the impulse, the Enterprise becomes embedded in the asteroid. What is their combined speed and direction? ## Diagrams 1. **Before Impact**: - A diagram shows the Earth in the lower half of the image with two vectors indicating the velocities of the ship \( v_A \) and the asteroid \( v_B \) leading to the impact. - The angle \( \theta \) between the direction of the ship’s velocity and the line of impact is marked as 60 degrees. 2. **After Impact**: - A second diagram shows the combined mass (ship and asteroid) moving in a new direction after the impact occurs, indicated by a dashed line. The collision point is marked, and the new path is distinctly diverging from the original paths.
Transcribed Image Text:# Problem Captain Jean-Luc Picard decides, as a last resort, to ram the asteroid (of mass \( m_B = 2,000 \, \text{kg} \)) with his starship (of mass \( m_A = 1,000 \, \text{kg} \)) in an attempt to deflect it from the planet. At the instant just before Capt. Picard decides to take action, the Enterprise and the asteroid are moving in opposite directions, at speeds \( v_A = 300 \, \text{m/s} \) and \( v_B = 500 \, \text{m/s} \), respectively. ### Part A: Capt. Picard commands his helmsman, Geordi La Forge, to match the asteroid's speed and intercept it at an angle \( \theta = 60 \, \text{deg.} \). Geordi sets the thruster to apply an impulse of \( \Delta t = 2 \) seconds but is unsure what direction the thrusters should point and how much force they should apply. What is the average force vector that Geordi must command during this interval? ### Part B: After the impulse, the Enterprise becomes embedded in the asteroid. What is their combined speed and direction? ## Diagrams 1. **Before Impact**: - A diagram shows the Earth in the lower half of the image with two vectors indicating the velocities of the ship \( v_A \) and the asteroid \( v_B \) leading to the impact. - The angle \( \theta \) between the direction of the ship’s velocity and the line of impact is marked as 60 degrees. 2. **After Impact**: - A second diagram shows the combined mass (ship and asteroid) moving in a new direction after the impact occurs, indicated by a dashed line. The collision point is marked, and the new path is distinctly diverging from the original paths.
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