Finding the speed of a bowling ball based on the length of the lane and sound.

[Naryeth]

Homework Statement

A bowling ball traveling with constant speed hits the pins at the end of a bowling lane 16.5 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.

Homework Equations

I'm not entirely sure.

The Attempt at a Solution

So, the bowling ball traveled 16.5m down the lane and the sound returned at 340 m/s, all in 2.60 seconds. By that logic, the bowling ball traveled to the end of the lane in 2.60s - the time it took for the sound to return.

That's as far as I've gotten and I'm completely lost. Any help is appreciated, thanks in advance :D

 

[Doc Al]

By that logic, the bowling ball traveled to the end of the lane in 2.60s - the time it took for the sound to return.

No, that doesn't follow.

Think of the process as having two parts:
(1) The bowling ball travels to the end of the lane (where it hits the pins and emits a sound).
(2) The sound travels back to the bowler.

Start by figuring out the time for part 2.

 

[Naryeth]

Ah, thank you. I've figured it out:

I know that sound can travel 340m in one second, therefore it traveled those 16.5 meters in 0.049 seconds (16.5/340). That means that the ball was rolling for 2.60-0.049 seconds, which is 2.551 seconds.

The ball traveled 16.5m in 2.251 seconds, so I just have to divide 16.5m/2.551s to get my final answer of 6.468m/s.

Thanks again!

 

[Doc Al]

Excellent! (Depending on how you round off intermediate steps, your final answer might be slightly different.)

 

[rwisz]

I would approach this problem by using the formula for speed, which is distance divided by time. In this case, the distance is 16.5 m and the time is 2.60 seconds minus the time it took for the sound to return, which is 2.60 seconds. This gives us a total time of 0 seconds for the ball to travel the 16.5 m down the lane.

Now, we can plug in these values into the formula for speed: speed = distance/time. So, the speed of the bowling ball would be 16.5 m / 0 s = undefined.

However, this answer does not make sense because we know that the ball is traveling at a constant speed and it takes time to travel down the lane. Therefore, we need to consider the fact that the sound takes time to travel back to the bowler's ears.

To account for this, we can use the fact that the speed of sound is 340 m/s. So, in the time it takes for the sound to travel back to the bowler's ears (2.60 seconds), the ball has traveled a distance equal to the speed of sound multiplied by the time it took for the sound to return. This gives us a distance of 340 m/s x 2.60 s = 884 m.

Now, we can subtract this distance from the original distance of 16.5 m to get the actual distance the ball traveled down the lane: 16.5 m - 884 m = -867.5 m. This negative distance indicates that the ball is actually traveling in the opposite direction, towards the bowler's hands.

To find the speed of the ball, we can use the formula speed = distance/time. The distance is now -867.5 m and the time is 2.60 seconds. This gives us a speed of -333.65 m/s.

However, this answer also does not make sense because it is a negative value. This indicates that there may be an error in the given information. It is possible that the time it takes for the sound to return is not 2.60 seconds, or the length of the lane is not 16.5 m.

In conclusion, based on the given information, the speed of the bowling ball cannot be accurately determined. Further information or clarification is needed to solve this problem.