# Further maths

A boat p moving due north at a speed of 5m/s.A boat Q is moving due east at a speed of 10m/s,calculate:(1)the magnitude of the velocity of P relative to Q,and(2)the bearing of the velocity of P relative to Q

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1. Subtraqct the Q velocity comonents from the p velocity components

North component of relative motion of P relative to Q: +5 m/s
East component of relative motion of P relative to Q: -10 m/s

relative velocity magnitude = sqrt[(5)^2 + (-10)^2]
= 11.2 m/s

Bearing: tan^-1(2) = 63.4 deg west of north, or 296.6 degrees clockwise from north

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