Two particles move in the same direction with measured speeds v₁ = (20.0 ± 0.2) m/s and v₂ = (18.0 ± 0.2) m/s. The maximum percentage error in their relative speed is:
Options

Question

Two particles move in the same direction with measured speeds v₁ = (20.0 ± 0.2) m/s and v₂ = (18.0 ± 0.2) m/s. The maximum percentage error in their relative speed is:

G1 Physics · Accepted Answer

The relative speed is vᵣ = v₁ - v₂ = 2.0 m/s. For subtraction, maximum absolute errors add: Δvᵣ = Δv₁ + Δv₂ = 0.2 + 0.2 = 0.4 m/s. Therefore percentage error = (0.4/2.0)×100 = 20%. The large error arises because the measured result is the difference of two nearly equal quantities.