University of The People Using a Vector Addition Simulation Questions SEE ATTACHMENTS You are participating in a road rally with your local classic car cl

University of The People Using a Vector Addition Simulation Questions SEE ATTACHMENTS

You are participating in a road rally with your local classic car club. Speed is how fast an object moves, and velocity is the rate at which an object changes position.

Part A

You drive 30 miles due east in a half hour. Then, you turn left and drive 30 miles north in 1 hour. What are your average speed and velocity, and what are the rectangular and polar coordinates of your position?

Part B

You have already traveled 30 miles east and then 30 miles north. To get back to the start, you travel 30 miles west in 1 hour and then 30 miles south in a half hour. What are your average speed and average velocity for the whole rally? Explain your answer.

Question 2

Consider a boat heading due east at 15 miles/hour. The water’s current is moving at 7.1 miles/hour at 45º south of east. Drag vectors for the boat and the current into the vector addition simulation.

Part A
What do Rx, Ry, , and |R| represent in terms of the force of the current, and what do they represent in terms of the forces moving the boat?

Part B

Using the vector addition simulation, what is the actual velocity of the boat? What is the actual direction the boat is traveling?

Robot Navigation

Self-navigating robots are very useful in the real world. Reducing the risk of human error by having a computer do tasks can increase the safety of transportation: Airplanes have systems that automate takeoffs and landings. Some cars can parallel park themselves. Cargo ships have autopilots. Mazes offer a challenge that can be directly translated to these situations.

In this task, you are developing navigation software for a company that makes robotic systems that can direct themselves. As a first-level test of the robot you are developing, you will have it navigate a maze.

Part A

When navigating the maze, the robot will only need to go north, south, east, and west. It can be useful to use the complex plane to represent these directions. When using the complex plane this way, we use numbers such that their magnitude is equal to 1. If we let the value i represent the robot facing due north, what values represent the robot facing east, south, and west?

Part B

The arrow at the maze entrance indicates that the robot will be heading east when it enters the maze. When programming the robot, let the complex number d represent the direction the robot is facing. As the robot changes direction, the value of d will also change; so, the value of d is dependent on where the robot is in the maze. At the start of the maze, what is the value of d?

Part C

While navigating the maze, the robot will need to be able to turn left and right. The first turn the robot will make is a left turn. What will the value of d be after the first turn?

Part D

When the robot makes a turn, it would be useful to have an operation to perform on d to represent this turn. This is because after making a turn, the new value of d will depend on the old value of d. Complete the table for the new values of d if the robot is turning left or right. Then determine an expression in terms of d that will give the new position if the robot turns left and another expression if the robot turns right. Type these expressions in the last row of the table.

Part E

Given the answer for part D, write an expression that will tell you the direction the robot is going if, in the course of its journey, it turns left 21 times and turns right 22 times. Does the order the robot makes the turns in matter for the purpose of knowing the direction it is finally facing? 4/23/2020
Unit Activity: Using a Vector Addition Simulation to Solve Problems
Task 1
Using a Vector Addition Simulation to Solve
Problems
Use this vector addition simulation to explore vectors and solve the following problems. First practice adding
some vectors to get comfortable with the simulation. Try the different styles under Component Display and
check the Show Grid box.
Question 1
You are participating in a road rally with your local classic car club. Speed is how fast an object moves, and
velocity is the rate at which an object changes position.
Part A
You drive 30 miles due east in a half hour. Then, you turn left and drive 30 miles north in 1 hour. What are your
average speed and velocity, and what are the rectangular and polar coordinates of your position?
Answer:
Characters used: 0 / 15000
Part B
You have already traveled 30 miles east and then 30 miles north. To get back to the start, you travel 30 miles
west in 1 hour and then 30 miles south in a half hour. What are your average speed and average velocity for the
whole rally? Explain your answer.
https://ſ1.app.edmentum.com/courseware-delivery/ua/5162/100001674/aHR0cHM6Ly9m MS5hcHAUZWRtZW50dW0uY29tL2xlYXJuZXIvc2Vjb25kYXJ… 1/3
4/23/2020
Unit Activity: Using a Vector Addition Simulation to Solve Problems
Answer:
Characters used: 0 / 15000
Question 2
Consider a boat heading due east at 15 miles/hour. The water’s current is moving at 7.1 miles/hour at 45° south
of east. Drag vectors for the boat and the current into the vector addition simulation.
Part A
What do Ry, Ry, 0, and [RI represent in terms of the force of the current, and what do they represent in terms
of the forces moving the boat?
Answer:
Characters used: 0 / 15000
https://f1.app.edmentum.com/courseware-delivery/ua/5162/100001674/aHR0cHM6Ly9m MS5hcHAUZWRtZW50dW0uY29tL2xlYXJuZXIvc2Vjb25kYXJ… 2/3
4/23/2020
Unit Activity: Using a Vector Addition Simulation to Solve Problems
Part B
Using the vector addition simulation, what is the actual velocity of the boat? What is the actual direction the
boat is traveling?
Answer:
Characters used: 0 / 15000
https://f1.app.edmentum.com/courseware-delivery/ua/5162/100001674/aHR0cHM6Ly9m MS5hcHAUZWRtZW50dW0uY29tL2xlYXJuZXIvc2Vjb25kYXJ… 3/3
4/23/2020
Unit Activity: Robot Navigation
Task 2
Robot Navigation
Self-navigating robots are very useful in the real world. Reducing the risk of human error by having a computer
do tasks can increase the safety of transportation: Airplanes have systems that automate takeoffs and landings
Some cars can parallel park themselves. Cargo ships have autopilots. Mazes offer a challenge that can be
directly translated to these situations.
In this task, you are developing navigation software for a company that makes robotic systems that can direct
themselves. As a first-level test of the robot you are developing, you will have it navigate a maze.
North
West
East
South
Part A
When navigating the maze, the robot will only need to go north, south, east, and west. It can be useful to use
the complex plane to represent these directions. When using the complex plane this way, we use numbers such
that their magnitude is equal to 1. If we let the value i represent the robot facing due north, what values
represent the robot facing east, south, and west?
https://ſ1.app.edmentum.com/courseware-delivery/ua/5162/100001674/aHR0cHM6Ly9m MS5hcHAUZWRtZW50dW0uY29tL2xlYXJUZXlvc2Vjb25kYXJ… 1/4
4/23/2020
Unit Activity: Robot Navigation
Answer:
Characters used: 0 / 15000
Part B
The arrow at the maze entrance indicates that the robot will be heading east when it enters the maze. When
programming the robot, let the complex number d represent the direction the robot is facing. As the robot
changes direction, the value of d will also change; so, the value of d is dependent on where the robot is in the
maze. At the start of the maze, what is the value of d?
Answer:
Characters used: 0/ 15000
Part C
https://f1.app.edmentum.com/courseware-delivery/ua/5162/100001674/aHROCHM6Ly9m MS5hcHAUZWRtZW50dWOuY29tL2xlYXJuZXIvc2Vjb25kYXJ… 2/4

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