A bowling ball traveling with constant speed hits the pins at the end of a bowling lane 15.5 m long. The bowler hears the sound of the ball hitting the pins 2.60 s after the ball is released from his hands. What is the speed of the ball? The speed of sound is 340 m/s. Answer to the nearest 0.001 m/s.

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To find the speed of the ball, we can use the formula for distance (d), speed (v), and time (t):

d = v * t

In this case, the distance is 15.5 m and the time is 2.60 s. However, since we're dealing with the time it takes for the sound to travel, we need to consider the time it takes for the ball to reach the pins minus the time it takes for the sound to reach the bowler's ears.

Let's calculate the time it takes for the ball to reach the pins. We'll call it t_ball:

t_ball = t - t_sound

Given that t is 2.60 s and t_sound is the duration it takes for the sound to reach the bowler's ears, we can rearrange the equation to solve for t_ball:

t_ball = 2.60 s - t_sound

Next, we'll calculate the time it takes for the sound to travel from the pins to the bowler's ears. The distance the sound travels is also 15.5 m. We can use the same formula as before, but this time the speed of sound is given as 340 m/s:

t_sound = d / v_sound

Substituting the known values, we get:

t_sound = 15.5 m / 340 m/s

Now we can substitute the value of t_sound back into the equation for t_ball:

t_ball = 2.60 s - (15.5 m / 340 m/s)

Finally, we can substitute the given distance (d), time (t_ball), and rearrange the formula to solve for speed (v):

v = d / t_ball

Plugging in the values, we have:

v = 15.5 m / t_ball

Now we can calculate the value of t_ball:

t_ball = 2.60 s - (15.5 m / 340 m/s)
t_ball ≈ 2.60 s - 0.045 m/s ≈ 2.555 s

Finally, we can calculate the speed:

v = 15.5 m / 2.555 s
v ≈ 6.067 m/s

Therefore, to the nearest 0.001 m/s, the speed of the ball is approximately 6.067 m/s.