QQuestionPhysics
QuestionPhysics
The typical baseball diamond is a square 90 ft long on each side. Suppose a player hits a home run and makes one complete trip from home plate, around the bases, and back to home plate.
Complete the table by finding the player's distance and displacement as he rounds the bases. Include the proper units. All angles are right angles. (Hint: You may need the Pythagorean theorem for 2nd base.)
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Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Baseball Diamond Geometry
The baseball diamond is a square with each side being 90 ft long. The bases form a perfect square, with right angles at each corner.
Step 3:: Calculate Distance from Home Plate to First Base
\text{Distance} = 90 \text{ ft}
\text{Displacement} = 90 \text{ ft}
Step 4:: Calculate Distance and Displacement from First Base to Second Base
\text{Displacement} = 90\sqrt{2} \text{ ft}
Using the Pythagorean theorem:
Step 5:: Calculate Distance and Displacement from Second Base to Third Base
\text{Distance} = 90 \text{ ft}
\text{Displacement} = 90 \text{ ft}
Step 6:: Calculate Distance and Displacement from Third Base to Home Plate
\text{Displacement} = 90\sqrt{2} \text{ ft}
Using the Pythagorean theorem:
Step 7:: Calculate Total Distance and Displacement
\text{Total Displacement} = 0 \text{ ft}$$ (since the player returns to home plate)
Total Distance: Total Displacement:
Final Answer
Here's the completed table: | Base Segment | Distance | Displacement | |-------------|----------|--------------| | Home to 1st | 90 ft | 90 ft | | 1st to 2nd | 90√2 ft | 90√2 ft | | 2nd to 3rd | 90 ft | 90 ft | | 3rd to Home | 90√2 ft | 90√2 ft | | Total | 180 + 180√2 ft | 0 ft |
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