. A rock thrown horizontally at a large bell 57.0 m away is heard to hit the bell 4.10 s later. If the speed of sound is 330 m/s, what was the speed (in meters/second) of the rock? (Disregard gravity.)
V*t = 57 m.
330 * t = 57,
t = 57/330 = 0.173 s. = Time for sound
to travel 57 m.
T = 4.10 - 0.173 = 3.927 s. = Time for rock to travel 57 m.
V*T = 57 m.
V = 57 / T = 57 / 3.927 = 14.5 m/s. =
Speed of rock.
To solve this problem, we can use the formula for the distance traveled by an object in uniform motion:
distance = speed × time
In this case, we know the distance (57.0 m) and the time (4.10 s) it took for the sound of the impact to reach the observer. We need to find the speed of the rock.
Since the rock was thrown horizontally, the horizontal component of its velocity remains constant throughout its flight. Therefore, the time it took for the rock to hit the bell is the same as the time it would take for the rock to travel horizontally for a distance of 57.0 m.
Let's use this information to calculate the speed of the rock:
speed = distance ÷ time
speed = 57.0 m ÷ 4.10 s
speed ≈ 13.9 m/s
So, the speed of the rock was approximately 13.9 meters/second.
To solve this problem, we can use the formula:
speed = distance / time.
First, let's find the time it took for the sound of the rock hitting the bell to reach the observer.
We are given that the speed of sound is 330 m/s, and the distance between the rock and the observer is 57.0 m. We can use the formula:
time = distance / speed.
Substituting the given values:
time = 57.0 m / 330 m/s.
Calculating:
time ≈ 0.173 s.
Now, let's find the time it took for the rock to reach the bell. We are given that this time is 4.10 s.
Since the sound and the rock reach the observer after this time, we can set up the equation:
total time = time for rock + time for sound.
Substituting the given values:
4.10 s = time for rock + 0.173 s.
Simplifying:
time for rock = 4.10 s - 0.173 s.
time for rock ≈ 3.93 s.
Now we can use this time and the distance between the rock and the bell to find the speed of the rock:
speed = distance / time.
Substituting the given values:
speed = 57.0 m / 3.93 s.
Calculating:
speed ≈ 14.52 m/s.
Therefore, the speed of the rock was approximately 14.52 m/s.