Question
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  1. 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?

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

  1. 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:
  2. 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:

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.
  1. Your Friend’s Position:
    • Starts from (0,0).
    • Runs 20 feet forward: (0, 20).
    • Runs 15 feet to the right: (15, 20).
  2. 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).
  1. Distance Calculation:
    Using the distance formula :
So,
Calculating:
So, you threw the baseball 10 feet!

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