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Advanced Maths (Vectors) AQA Level, please help?

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Starting simultaneously from the same spot, O, Alvin and Bernard set out across a field in the gog. Alvin travels with velocity i + 2 j m/s and Bernard with velocity 3i + j m/s, To avoid losing each other, they hold opposite ends of 90 m string.
a) At what speed alvin travels
b) Find the direction of travel of the two people and hence the angle between their path
c) Find the position vector OA and OB at t sesonds, and hence the vector AB at that time
d)Find the value of t for which the dtring become taut

  • Advanced Maths (Vectors) AQA Level, please help? -

    Alvin speed = sqrt (1^2 + 2^2) = sqrt (5)

    tan Alvin = 2/1 so angle Alvin = 63.4 deg

    tan Bernard = 1/3 so angle = 18.4
    so
    angle between = 63.4 - 18.4 = 45 degrees

    OA = t i + 2t j
    OB = 3t i + t j

    AB = 2 t i -1 t j

    d = sqrt ( 4t^2 + t^2) = t sqrt (5)
    90 = t sqrt 5
    t = 40.3 seconds

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