Question
- You and your friend are standing back-to-back. Your friend runs 20
feet forward and then 15 feet right. At the same time, you run 12 feet
forward and then 9 feet right. You stop and throw a baseball to your
friend, who catches it. How far did you throw the baseball?
feet forward and then 15 feet right. At the same time, you run 12 feet
forward and then 9 feet right. You stop and throw a baseball to your
friend, who catches it. How far did you throw the baseball?
Ask by Macdonald Chen. in the United States
Jan 30,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
You threw the baseball 40 feet.
Solution
To determine how far you threw the baseball, we’ll analyze the movements of both you and your friend on a coordinate system.
Step 1: Establish a Coordinate System
- Origin (0,0): Starting point where both of you are back-to-back.
- Your Orientation:
- Forward: Positive y-direction.
- Right: Positive x-direction.
- Friend’s Orientation:
- Forward: Negative y-direction.
- Right: Negative x-direction.
Step 2: Calculate Final Positions
-
Friend’s Movement:
- 20 feet forward: Since your friend is facing the negative y-direction, this corresponds to
y-units. - 15 feet right: Facing opposite to your positive x-direction, this is
x-units.
Friend’s Final Position: - 20 feet forward: Since your friend is facing the negative y-direction, this corresponds to
-
Your Movement:
- 12 feet forward: In your positive y-direction, this is
y-units. - 9 feet right: In your positive x-direction, this is
x-units.
Your Final Position: - 12 feet forward: In your positive y-direction, this is
Step 3: Determine the Distance Between Final Positions
Use the distance formula between two points
and
:
Plugging in the values:
Final Answer
You threw the baseball 40 feet.
Answered by UpStudy AI and reviewed by a Professional Tutor
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The Deep Dive
To find out how far you threw the baseball, we need to figure out your final positions and then use the distance formula.
-
Your Friend’s Position:
- Starts from (0,0).
- Runs 20 feet forward: (0, 20).
- Runs 15 feet to the right: (15, 20).
-
Your Position:
- Starts from (0,0).
- Runs 12 feet forward: (0, 12).
- Runs 9 feet to the right: (9, 12).
Now we have your friend’s coordinates as (15, 20) and yours as (9, 12).
- Distance Calculation:
Using the distance formula:
So,
Calculating:
So, you threw the baseball 10 feet!