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 77 meters from you. You hear the "clunk" of impact 0.56 seconds after you "let fly." If the speed of sound on that particular day is 325 m/s, how fast must the ball bearing be traveling?
I don't know how to start this. As a hit it said "Average speed is total distance divided by total time The time it takes for the ball bearing to strike the steel drum is the total time minus the time it takes for the sound to return." but I'm not sure how that could help.
Thanks!
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Verified answer
Assuming this is a one-dimensional problem where the motion is purely
horizontal and ideal, then the initial speed if the ball-bearing (Vь) is:
Time of ball-bearing to target = Tь = 77 ⁄ (Vь)
Time of sound to return = Ts = 77 ⁄ (Vs)
= 77 ⁄ 325 ... in seconds
Tь + Ts = 0.56
(77 ⁄ Vь) + (77 ⁄ 325) = 0.56
(77 ⁄ Vь) = 0.3231
Vь = 238 meters/sec
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