Question

The graph represents the distance a major league outfielder throws a baseball. He can throw as fast as 105 miles per hour or 154 feet per second which equation represents this scenario

Answer 1

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.**

1. Given speed: 105 miles per hour
2. Convert miles to feet:
\[
105 \text{ miles} = 105 \times 5280 \text{ feet}
\]

3. 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.