Need help w/Speed of a Slingshot problem

[junesmrithi]

Question: To find the speed of a ball bearing launched from a wrist rocket (sling-shot) you take aim at a 55 gallon steel drum exactly 78 meters from you. You hear the "clunk" of impact 0.7 seconds after you "let fly." If the speed of sound on that particular day is 330 m/s, how fast must the ball bearing be traveling?

 

[cristo]

This is clearly a homework question, so PF rules state that you must show your work before we can help you. What thoughts do you have on the question?

Also, in future, please post such questions in the homework forums.

 

[m2003]

To find the speed of the ball bearing, we can use the formula v = d/t, where v is the velocity, d is the distance, and t is the time. In this case, the distance is 78 meters and the time is 0.7 seconds. Plugging these values into the formula, we get v = 78/0.7 = 111.43 m/s.

However, this is not the speed of the ball bearing, as we need to consider the speed of sound on that particular day. The speed of sound can affect the time it takes for the "clunk" of impact to reach our ears. In this case, the speed of sound is given as 330 m/s.

To account for the speed of sound, we need to subtract the distance traveled by the sound from the total distance. Since sound travels at 330 m/s, in 0.7 seconds it would have traveled 0.7*330 = 231 meters. Therefore, the actual distance traveled by the ball bearing is 78 - 231 = -153 meters.

Using this new distance in the formula, we get v = -153/0.7 = -218.57 m/s. This is the velocity of the ball bearing, but it is a negative value because the ball bearing is traveling towards the drum. To get the absolute value, we can take the magnitude of this velocity, which is approximately 218.57 m/s.

Therefore, the ball bearing must be traveling at a speed of approximately 218.57 m/s to reach the drum in 0.7 seconds, taking into account the speed of sound on that particular day.