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.)