The sides of a baseball diamond are 27 meters in length. What is the average speed of a baseball player who runs from first base to third base in a time of 7.2 seconds?
We’ll begin by drawing a quick sketch of the information given to us in the question. We have our baseball diamond, and we know that the sides are 27 meters long. We’re told that the player starts at first base and runs to third base. That means that they first run along this side of the diamond from first base to second base and then they run along this side from second base to third base. Since we’re told that the sides of the diamond are 27 meters in length, then we know that the length of the side between the second base and the third base is 27 meters, just like the length of the side between first and second base.
The question asks us to find the average speed of the player. We can recall that speed is defined as the distance traveled divided by the time taken to cover that distance. If we label the speed 𝑠, the distance 𝑑, and the time 𝑡, then we can write this more concisely as 𝑠 is equal to 𝑑 divided by 𝑡. Now we’re looking to calculate the value of the speed 𝑠. The question tells us that the player takes a time of 7.2 seconds to run from first base to third base. So we can say that 𝑡 is equal to 7.2 seconds. We also know that the sides of this diamond are 27 meters long and that the player runs along two of these sides, firstly the side from first base to second base and then the side from second base to third base.
Since each of these sides is 27 meters, we can say that the distance 𝑑 covered by the player is equal to the 27 meters from the first side plus the 27 meters from the second side. When we do the sum 27 meters plus 27 meters, we find that 𝑑 is equal to 54 meters. So, we know the values of the distance 𝑑 covered by the player and the time 𝑡 taken for them to cover that distance. So now we can substitute those values into this formula to calculate the average speed of the player. Doing this gives us that the speed 𝑠 is equal to the distance of 54 meters divided by the time of 7.2 seconds. When we divide 54 meters by 7.2 seconds, we get a result of 7.5 meters per second.
And so we have our answer that the average speed of the baseball player is 7.5 meters per second.