Ahungry 12.5 kg predator fish is coasting from west to east at 70.0 cm/s when it suddenly swallows a 1.30 kg fish swimming from north to south at 3.40 m/s . part a)
find the magnitude of the velocity of the large fish just after it snapped up this meal. neglect any effects due to the drag of the water.
part b)
find the direction of the velocity of the large fish just after it snapped up this meal.

Explanation:

Momentum of bigger fish = mv

= 12.5 x 0.7 = 8.75 kg.m/s

In vector form in will be in - ve x direction so

momentum = - 8.75 i

Similarly momentum of small fish

= 1.3 x 3.4 = 4.42 kg.m/s

Since the fish is going towards south so in vector form momentum

= -4.42j

Total momentum of bigger fish in vector form

= - 8.75 - 4.42j

Magnitude of momentum of bigger fish required

= √ 8.75² + 4.42² = 9.80  kg m/s

velocity of bigger fish = momentum / total mass of bigger fish

= 9.8/(12.5+1.3) = .71 m/s

= 71 cm/s

Its direction will be towards south- east making an angle as follows with east towards south

Tan θ = y component / x component

= 4.42/ 8.75 = 0.505

θ = 27 degree  south of east.