To convert the speed of the outfielder's throw into feet per second, we can use the fact that 1 mile is equal to 5280 feet and 1 hour is equal to 3600 seconds.
Step 1: Convert miles per hour to feet per second.
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Given speed: 105 miles per hour
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Convert miles to feet: \[ 105 \text{ miles} = 105 \times 5280 \text{ feet} \]
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We convert hours to seconds: \[ 1 \text{ hour} = 3600 \text{ seconds} \]
Now, calculate the speed in feet per second: \[ \frac{105 \times 5280 \text{ feet}}{3600 \text{ seconds}} \]
Calculating this: \[ 105 \times 5280 = 554400 \text{ feet per hour} \] \[ \frac{554400}{3600} \approx 154 \text{ feet per second} \]
The conversion confirms that 105 miles per hour is indeed approximately 154 feet per second.
Step 2: Find relevant equations to represent his throwing scenario.
Since the throw's speed has been established as 154 feet per second, the distance \( d \) that the ball travels can be modeled as a function of time \( t \). The basic equation you'd use in this scenario (assuming constant velocity without considering air resistance) is:
\[ d = r \cdot t \]
Where:
- \( d \) is the distance thrown (in feet),
- \( r \) is the rate of throwing (which we've found to be 154 feet per second),
- \( t \) is the time (in seconds).
Substituting the known value into the equation, we get:
\[ d = 154 \cdot t \]
Thus, the equation that represents the outfielder's throw in feet as a function of time in seconds is:
\[ d = 154t \]
This equation models the distance thrown based on the throw speed of the outfielder.
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