A student throws a baseball at a large gong 73 m away and hears the sound of the gong 1.7744 s later. The speed of sound in air is 330 m/s.
What was the average speed of the base-
ball on its way to the gong? (For simplicity, assume its trajectory to be a straight line.)
Answer in units of m/s.
Well, the average speed of the baseball can be calculated by dividing the total distance traveled by the time it took. In this case, the distance traveled is 73 m and the time it took is 1.7744 s. So, if I do the math correctly (and I always do!), the average speed of the baseball would be... drumroll, please... approximately 41.10 m/s! Now, that's some serious speed for a baseball!
To find the average speed of the baseball on its way to the gong, we need to divide the distance traveled by the time taken.
Given:
Distance to the gong (d) = 73 m
Time taken to hear the sound (t) = 1.7744 s
The speed of sound in air (v) = 330 m/s
The time taken to hear the sound is the total time for the baseball to travel to the gong and for the sound to travel back to the student.
The time taken for the baseball to travel to the gong (t_baseball) can be found by subtracting the time taken for the sound to travel back from the total time:
t_baseball = t - (2 * (d / v))
Substituting the given values:
t_baseball = 1.7744 s - (2 * (73 m / 330 m/s))
Simplifying:
t_baseball = 1.7744 s - (2 * 0.2212 s)
t_baseball = 1.7744 s - 0.4424 s
t_baseball = 1.332 s
Now, we can find the average speed of the baseball by dividing the distance traveled by the time taken:
Average speed (v_average) = d / t_baseball
Substituting the given values:
v_average = 73 m / 1.332 s
Calculating:
v_average ≈ 54.76 m/s
Therefore, the average speed of the baseball on its way to the gong is approximately 54.76 m/s.
To find the average speed of the baseball on its way to the gong, we can use the formula:
Average speed = Total distance / Total time
In this case, the total distance is the distance from the student to the gong, which is given as 73 m. The total time is the time it takes for the baseball to reach the gong, which is given as 1.7744 s.
Now we can substitute these values into the formula:
Average speed = 73 m / 1.7744 s
Calculating this, we get:
Average speed = 41.032 m/s
Therefore, the average speed of the baseball on its way to the gong is 41.032 m/s.
Let the average speed be V, in m/s.
73/V + 73/330 = 1.7744 s
73/V = 1.7744 - 0.2212 = 1.5532
V = 47.0 m/s