Speed of bowling ball involving speed of sound

In summary, the problem involves a bowling ball traveling with constant speed and hitting pins at the end of a 16.5 m long bowling lane. The sound of the ball hitting the pins is heard by the bowler 2.5 s after the ball is released. Using the kinematic equations and the speed of sound (340 m/s), the time for sound to travel from the pins to the bowler is calculated to be 0.049 s. Subtracting this from the total time (2.5 s), the time for the ball to hit the pins is found to be 2.45 s. The velocity of the ball is then calculated to be 6.73 m/s.
  • #1
Entr0py
102
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?

Homework Equations


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

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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  • #2
Hint : start by working out the time taken for sound to travel one direction back from pins to bowler .
 
  • #3
Nidum said:
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?
 
  • #4
Entr0py said:
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?
 
  • #5
So how long does ball take to travel from bowler to pins ?
 
  • #6
Nidum said:
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.
 
  • #7
Nidum said:
So how long does ball take to travel from bowler to pins ?
.049 s.
 
  • #8
Your answer of 2,45 sec travel time and 6,73 M/sec velocity is correct .
 

Related to Speed of bowling ball involving speed of sound

1. What is the speed of sound?

The speed of sound is the distance that sound waves travel per unit time. It is approximately 343 meters per second in dry air at room temperature.

2. How does the speed of sound affect the speed of a bowling ball?

The speed of sound has a direct effect on the speed of a bowling ball. As the ball travels through the air, it creates sound waves. These sound waves can either slow down or speed up the ball, depending on the direction in which they are traveling.

3. Can the speed of sound be used to measure the speed of a bowling ball?

Yes, the speed of sound can be used to indirectly measure the speed of a bowling ball. By measuring the time it takes for the sound of the ball to reach a certain point, the speed of the ball can be calculated using the known speed of sound.

4. How does the density of the medium affect the speed of sound and the bowling ball?

The density of the medium, such as air, can affect the speed of sound and the bowling ball. In denser mediums, such as water, sound travels faster and can therefore impact the speed of the ball differently. Additionally, a denser medium can create more resistance for the ball, slowing it down.

5. Can the speed of sound be faster than the speed of a bowling ball?

No, the speed of sound is generally much slower than the speed of a bowling ball. While the speed of sound can vary based on the medium it is traveling through, the average speed is still much slower than the speed of a bowling ball, which can reach up to 30 miles per hour.

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