Two particles move along mutually perpendicular directions with speeds u and v. Their relative speed is V = √(u² + v²). If the maximum absolute errors are Δu and Δv, the maximum relative error in V is:
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Question

Two particles move along mutually perpendicular directions with speeds u and v. Their relative speed is V = √(u² + v²). If the maximum absolute errors are Δu and Δv, the maximum relative error in V is:

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G1 Physics · Accepted Answer

V = (u² + v²)¹ᐟ². Differentiate: dV = (u du + v dv)/√(u² + v²). Dividing by V = √(u² + v²), we obtain dV/V = (u du + v dv)/(u² + v²). For maximum error, take magnitudes: ΔV/V = (uΔu + vΔv)/(u² + v²).