Normal 1 No Spac... Heading 1 Heading 2 Title Subtitle A Paragraph IN Styles Mission on Mars You are on the Mars mission planning team that will determine the best route for a crew to use on the first trip using the new Mars Exploration Rover (MER). This exploration mission will include traveling from the crater Bada to the crater Babkin on the surface of Mars. Late projects will lose 10 points per day, including weekends. MER is at habitat A on the map near the Bada crater. Its mission for the day is to drive to the rim of the Babkin crater to collect rock samples. Rocks can be collected at any point along the edge of the crater (along segment PQ on the map). Before MER and the crew return to the habitat, they must also stop at location B on the map in order to reset a seismic sensor that has been gathering data about the interior of the Moon. All distances are denoted on the diagram below. 17 km Babkin Crater Q B 19 km 28.5 km Bada Crater O Hi IN W AeAav Po AaBbCcDd AaBbCcDd AaBbC( AaBbCc[ Ad D AaBbCCD 1 Normal 1 No Spac.. Heading 1 Heading 2 Title Subtitle A Paragraph Styles In this project, you will solve the following two problems: 1. Minimal Path Problem: Find the best location for point D on PQ so that the total travel DISTANCE for AD + DB for the MER is mimimized. 2. Minimal Time Problem: Find the best location for point T on PQ so that the total travel TIME for AT+ TB is minimized. Part 1: Minimal Path Problem Your mission planning team must find the shortest total path for MER to travel for this exploration. The crew will start at habitat A and travel to a point along the Babkin crater (on segment PQ) to collect rock samples. This point will be denoted as point D. Then, the crew will take MER from that point D to location B to reset the seismic sensor. 1. Create a scale drawing for the mission the graph provided below. Point P (from the diagram on the first page) is located at the origin, segment AP lies on the x-axis, and segment PQ lies on the y-axis. Chose a point on PQ along the Babkin Crater that you think would give the shortest total distance. Label that point G on the graph, and create the path traveled using the color BLUE. This will serve as your first prediction, and you will be asked how this compares to the solution you ultimately find at the end of this task. FO O 9 N W Ae F4 F5 F6erences Mailings Aav AaBbCcDd AaBbCcDd AaBbC( AaBbCct AaB AaBbCCD AaBb 1 Normal No Spac... Heading 1 Heading 2 Title Subtitle Subtle A Paragraph Styles Your mission planning team must find the shortest total path for MER to travel for this exploration. The crew will start at habitat A and travel to a point along the Babkin crater (on segment PQ) to collect rock samples. This point will be denoted as point D. Then, the crew will take MER from that point D to location B to reset the seismic sensor. 1. Create a scale drawing for the mission the graph provided below. Point P (from the diagram on the first page) is located at the origin, segment AP lies on the x-axis, and segment PQ lies on the y-axis. Chose a point on PQ along the Babkin Crater that you think would give the shortest total distance. Label that point G on the graph, and create the path traveled using the color BLUE. This will serve as your first prediction, and you will be asked how this compares to the solution you ultimately find at the end of this task. 16 12 Focus O N X W Ae F4 F5 F6 F7 F8AaBbCcDd AaBbCcDd AaBbC( AaBbCct Aa B AaBbCCD AaBb 1 Normal I No Spac... Heading 1 Heading 2 Title Subtitle Subtle Paragraph Styles 2. Working with your mission planning team, use optimization techniques to algebraically determine the best location for point D so that the total DISTANCE MER travels is minimized. Round your solution to the nearest hundredth. Verify that your result is the location of a minimum by testing the endpoints as well as using either the First Derivative Test or Second Derivative Test (your choice). Make sure to clearly show all work, including the feasible domain. Be sure to test endpoints as well. Focus N X W Ae F4 F5 F6 F7 F8 F9 F10ences Mailings Review View Help av Ap FETEENT AaBbCcDd AaBbCcDd AaBbC( AaBbCct Ad B AaBbCCD AaBbCcD 1 Normal 1 No Spac.. Heading 1 Heading 2 Title Subtitle Subtle Er A v Paragraph Styles 3. What is this minimum distance traveled? Round to the nearest hundredth. 4. Show your solution on your mission graph on page 2 by highlighting or labeling MER's path for the shortest distance traveled using the color. GREEN. How close was your prediction point G for the shortest total distance to your actual solution? Part 2: Minimal Time Problem The average speed of MER is 8.9 km/hr with an empty payload. With a full payload of rocks, the average speed drops to 5.5 km/hr. Find the best location for point T so that you minimize the total travel TIME for the distance AT+ TB. Recall that t - ". 5. Working with your mission planning team, determine the best location for point T so that the total time it take for MER to complete the mission is minimized. Use technology to complete this portion. Show your setup for the equations, but you do not need to show the actual calculations. Be sure to test the endpoints as well. Round your solution to the nearest hundredth. Focus O 9 N W Ae F4 F5 F6 F7 F8 FO F1AaBbCcDd AaBbCcDd AaBbC( AaBbCcE Ad B AaBbCCD AaBb Aa 1 No Spac... Heading 1 Heading 2 Title Subtitle Subtle Normal Styles Paragraph 6. What is the minimum time for this mission? 7. Show your solution on your mission graph by highlighting or labeling MER's path for the shortest TIME traveled using the color RED. 8. Are the solutions for the best location to collect rocks in order to minimize distance and minimize time the same? If they are different, provide a possible explanation for why this is the case. Focus O N X W Ae F4 F5 F6 F7 F8 F9 F10 KK F11 F12 Pr