Skier Boat A B 10 C + Dock You are an engineer who has been tasked...

Transcribed Image Text:

Skier Boat A B 10 C + Dock You are an engineer who has been tasked to design a water-skiing activity in an amusement park (see figure). Water skiing is a popular summertime activity across Canada. A skier, holding onto a towrope, is pulled across the water by a motorboat. The pool is 50 meters by 50 meters. Set up a coordinate system with the Southwest corner located at (0,0), the x-axis in the West-East direction and y-axis in the North-South direction. A dock is located at position (30,20). The top view is shown in the figure. You need to create a parabolic path for the motorboat leading ride. Then the rider will let go of the towrope and complete the rest in a straight line. a) Choose your own path - the figure is only an example. Create a quadratic function to model your path. Show how you solve it mathematically. Keep in mind that you want to 1) use most of the area of the pool, so the rider has a good view 2) pass the dock from the West side. b) To increase the excitement, find three points in your path, A, B, and C. You need to choose your points. Again, they are just examples in the figure. The rider can choose to let go of the towrope at one of them, A, B or C. Then they will continue the ride in a straight line. Use linear functions to model the paths after the rider lets go of the towrope. c) Write your answers from part b) as vector equations for lines. d) Find the direction the rider is heading to in each case. Use direction bearing. e) Find the shortest distances between the dock and each of the three straight paths. f) At what point should the rider release the towrope to head straight for the dock? What is the direction the rider heads in? g) The rider slides from the point you find in f) to the dock. What is the distance in the NORTH direction of this straight trajectory? Use a projection to find. h) List the assumptions you have made to solve this problem. ROUND all your answers to two decimal places when necessary. Skier Boat A B 10 C + Dock You are an engineer who has been tasked to design a water-skiing activity in an amusement park (see figure). Water skiing is a popular summertime activity across Canada. A skier, holding onto a towrope, is pulled across the water by a motorboat. The pool is 50 meters by 50 meters. Set up a coordinate system with the Southwest corner located at (0,0), the x-axis in the West-East direction and y-axis in the North-South direction. A dock is located at position (30,20). The top view is shown in the figure. You need to create a parabolic path for the motorboat leading ride. Then the rider will let go of the towrope and complete the rest in a straight line. a) Choose your own path - the figure is only an example. Create a quadratic function to model your path. Show how you solve it mathematically. Keep in mind that you want to 1) use most of the area of the pool, so the rider has a good view 2) pass the dock from the West side. b) To increase the excitement, find three points in your path, A, B, and C. You need to choose your points. Again, they are just examples in the figure. The rider can choose to let go of the towrope at one of them, A, B or C. Then they will continue the ride in a straight line. Use linear functions to model the paths after the rider lets go of the towrope. c) Write your answers from part b) as vector equations for lines. d) Find the direction the rider is heading to in each case. Use direction bearing. e) Find the shortest distances between the dock and each of the three straight paths. f) At what point should the rider release the towrope to head straight for the dock? What is the direction the rider heads in? g) The rider slides from the point you find in f) to the dock. What is the distance in the NORTH direction of this straight trajectory? Use a projection to find. h) List the assumptions you have made to solve this problem. ROUND all your answers to two decimal places when necessary.