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Ship Collision Project: Two ships are steaming through the fog. At time t = 0 minutes
Chapter 13, Problem 4(choose chapter or problem)
Ship Collision Project: Two ships are steaming through the fog. At time t = 0 minutes, their positions and velocities are Ship A: Point (x, y) = (2000, 600), velocity 500 m/min on an angle of \(140^{\circ}\) Ship B: Point (x, y) = (200, 300), velocity 400 m/min on an angle of \(80^{\circ}\)
a. Write parametric equations for the position (x, y) of each ship, with x and y in meters and the parameter t in minutes.
b. Plot the parametric equations for both ships on the same screen. Use simultaneous mode so that you can see where each ship is with respect to the other as the graphs are being plotted. Based on what you observe, do the ships collide, almost collide, or miss each other by a significant amount?
c. Use the distance formula to help you write a Cartesian equation for the distance between the ships as a function of time. Plot this function on another screen and sketch the result.
d. By appropriate operations on the function of part c, find numerically the time the ships are the closest and how close they get. Based on your answer, should the ships have changed their courses to avoid a collision, or will they miss each other by a safe distance?
e. In July 1956, there was a serious collision between the ships Andrea Doria and Stockholm. On the Internet or in some other reference source, find out what happened.
Questions & Answers
QUESTION:
Ship Collision Project: Two ships are steaming through the fog. At time t = 0 minutes, their positions and velocities are Ship A: Point (x, y) = (2000, 600), velocity 500 m/min on an angle of \(140^{\circ}\) Ship B: Point (x, y) = (200, 300), velocity 400 m/min on an angle of \(80^{\circ}\)
a. Write parametric equations for the position (x, y) of each ship, with x and y in meters and the parameter t in minutes.
b. Plot the parametric equations for both ships on the same screen. Use simultaneous mode so that you can see where each ship is with respect to the other as the graphs are being plotted. Based on what you observe, do the ships collide, almost collide, or miss each other by a significant amount?
c. Use the distance formula to help you write a Cartesian equation for the distance between the ships as a function of time. Plot this function on another screen and sketch the result.
d. By appropriate operations on the function of part c, find numerically the time the ships are the closest and how close they get. Based on your answer, should the ships have changed their courses to avoid a collision, or will they miss each other by a safe distance?
e. In July 1956, there was a serious collision between the ships Andrea Doria and Stockholm. On the Internet or in some other reference source, find out what happened.
ANSWER:Step 1 of 6
As per the given data, we have,
For ship A:
Point \(\left( {x,y} \right) = \left( {2000,600} \right)\)
velocity \(500\,m/\min \) at an angle of \(140^\circ \).
For ship B:
Point \(\left( {x,y} \right) = \left( {200,300} \right)\)
velocity \(400\,m/\min \) at an angle of \(80^\circ \).