# Speed of bowling ball involving speed of sound

#### Entr0py

1. Homework Statement
A bowling ball traveling with a 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 pins 2.5 s after ball is released from his hands. What is the speed of ball, assuming speed of sound is 340 m/s?

2. Homework Equations
the kinematic equations
x=x0+v0t+.5at^2
v=v0+at
vf^2=v0^2+2ax

3. The Attempt at a Solution
Well, I thought that somehow I could use the time it takes for the sound wave to travel up and down the bowling lane, which is (33 m)/(340 m/s)= about .097 s. See I can picture the problem in my head, but I don't know how to get t for the ball in order to find the speed.

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#### Nidum

Gold Member
Hint : start by working out the time taken for sound to travel one direction back from pins to bowler .

#### Entr0py

Hint : start by working out the time taken for sound to travel one direction back from pins to bowler .
Are you asking the time it takes sound to travel just to end of lane?

#### Entr0py

Are you asking the time it takes sound to travel just to end of lane?
Then wouldn't the time be about .049 s to travel from the pins to you?

#### Nidum

Gold Member
So how long does ball take to travel from bowler to pins ?

#### Entr0py

Hint : start by working out the time taken for sound to travel one direction back from pins to bowler .
Now, since I hear the ball hitting the pins 2.5 s after I throw it, then the time it takes the ball to hit the pins= 2.5 s - .049 s =2.45 s. Now to find velocity I do v= change in r/change in t= 16.5 m/2.45 s= 6.73 m/s is speed of ball.

#### Entr0py

So how long does ball take to travel from bowler to pins ?
.049 s.

#### Nidum

Gold Member
Your answer of 2,45 sec travel time and 6,73 M/sec velocity is correct .

"Speed of bowling ball involving speed of sound"

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