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Can someone help me with my physics homework.?
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 80 meters from you. You hear the "clunk" of impact 0.72 seconds after you "let fly." If the speed of sound on that particular day is 335 m/s, how fast must the ball bearing be traveling?
Given d=80m, v.s=335m/s, g=9.81m/s²
Assume even ground and neglect air resistance.
The time for the sound to travel is:
t.s = d/v.s = 0.2388 s
Since we know distance & time, we can find speed & angle from equations (from ref. below):
d = (2v²/g)sinθcosθ = 80m
t = (2v/g)sinθ = 0.72-0.24 = 0.48s
Solve each for v, then set them equal to get:
dg/(2sinθcosθ) = (gt/2sinθ)²
Solving for θ simplifies to:
θ = atan(gt²/2d) = 0.81°
Now solve for v using either equation above:
v = gt/2sinθ = 167 m/s (373mph)
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