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The ant's resultant velocity is 0.51 m/s at 78.7°
Since the ant is moving with a velocity of 0.1 m/s in the +x direction relative to the treadmill, and the treadmill is moving 0.5 m/s in the +y direction, the magnitude of the resultant velocity of the ant relative to the ground (since both directions are perpendicular) is thus
V = √(x² + y²)
= √[(0.1 m/s)² + (0.5 m/s)²]
= √[0.01 m²/s² + 0.25 m²/s²]
= √(0.26 m²/s²)
= 0.51 m/s.
The direction is Ф = tan⁻¹(y/x)
= tan⁻¹(0.5 m/s ÷ 0.1 m/s)
= tan⁻¹(5)
= 78.69°
≅ 78.7°
The ant's resultant velocity is 0.51 m/s at 78.7°
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