Student throws a baseball at a large gong 79 miles away and hears the sound of gong 2.63333 seconds later. The speed of sound in air is 330 miles per second. What was the average speed of baseball on its way to gong ?
To find the average speed of the baseball on its way to the gong, we need to calculate the total distance traveled by the baseball.
We are given that the speed of sound in air is 330 miles per second. Since the time it took for the sound to reach the student was 2.63333 seconds, we can calculate the distance the sound traveled by multiplying the speed of sound by the time:
Distance covered by sound = Speed of sound * Time
Distance covered by sound = 330 miles/second * 2.63333 seconds
Distance covered by sound = 867.9999 miles
Now, since we know the total distance covered by the sound is the same as the distance between the student and the gong, which is 79 miles, we can find the distance covered by the baseball:
Distance covered by baseball = Total distance covered - Distance covered by sound
Distance covered by baseball = 79 miles - 867.9999 miles
Distance covered by baseball = -788.9999 miles
Since a distance cannot be negative, we can conclude that the baseball did not reach the gong. Therefore, we cannot calculate the average speed of the baseball on its way to the gong with the given information.
To find the average speed of the baseball on its way to the gong, we need to know the time it took for the baseball to reach the gong and the distance between the student and the gong.
In this scenario, we are given that the sound of the gong was heard 2.63333 seconds later. This time represents the time it took for the sound to travel from the gong to the student. Since sound travels at a speed of 330 miles per second, we can calculate the distance between the student and the gong by multiplying the speed of sound by the time it took for the sound to reach the student:
Distance = Speed × Time
Distance = 330 miles per second × 2.63333 seconds
Calculating this gives us:
Distance = 868 miles
So, the distance between the student and the gong is 868 miles.
However, we still need to determine the time it took for the baseball to reach the gong from the student. The question states that the gong is 79 miles away from the student. Let's call this time t.
Distance = Speed × Time
79 miles = Speed × t
To find the time t, we need to divide the distance by the average speed of the baseball:
t = 79 miles / Speed
Now, we can substitute the calculated distance of 868 miles to find t:
t = 79 miles / 868 miles
Calculating this gives us:
t = 0.09109 seconds
Therefore, the time it took for the baseball to reach the gong is approximately 0.09109 seconds.
Now that we have both the distance and the time, we can calculate the average speed of the baseball using the formula:
Average Speed = Distance / Time
Average Speed = 79 miles / 0.09109 seconds
Calculating this gives us:
Average Speed ≈ 867.88 miles per second
Therefore, the average speed of the baseball on its way to the gong is approximately 867.88 miles per second.