Question

A sailor in a boat, which is going due east with a speed of 8 m/s, observes that a submarine is heading towards north at a speed of 12m/s and sinking at a rate of 2 m/s. the commander of submarine observes a helicopter ascending at a rate of 5 m/s and heading towards west with 4m/s. find the actual speed of the helicopter and its speed w.r.t. boat

Answer 1

let the direction of  East be denoted by x axis with unit vector i.let the direction of North be y axis with  unit vector k.Let the vertical direction be  z axis with u v = k.
b = boat,   sb = submarine wrt boat,  hb = helicopter wrt boat
Vb = 8 i  m/s Vsb = 12 j - 2 k  m/s=>  Vs = Vsb + Vb = 12 j + 8 i - 2 k   m/s  =>  speed = 2√53  m/s
Vhs = 5 k - 4 i=> Vh = Vhs + Vs = 4 i + 2 j + 3 k=>  Magnitude = √29  m/s
Vhb = Vh - Vb = -4 i + 2j + 3 k    => magnitude of speed = √29 m/s