Let be the unit vectors along east and south.
The velocity of ship P,
The velocity of ship Q,
∴
and
Thus the velocity of ship Q w.r.t. P is 50 km/hr due 37° west of south.
Velocity of ship A,
Velocity of ship B,
The relative velocity of B w.r.t. A is,
Magnitude of velocity is given by,
∴
and
So, relative velocity of B w.r.t. A is 25.6 km/h due
The distance between two ships after 5 hours,
S = Vt
= 25.6 x 5
= 128km.
Let the velocity of ejecting gases with respect to ground be .
Velocity of jet plane,
Velocity of ejected products w.r.t. jet plane,
Now, relative velocity of ejecting gases w.r.t the jet plane is given by,