Question

A boat with a total mass of 500 kg is travelling north on a lake. The motor of the boat provides a force of 400 N in the northerly direction. The wind blows 30◦ away from the northerly direction slightly towards east. It exerts a force of 300 N on the boat. Find the acceleration of the boat including magnitude and direction. Assume that the friction between the boat and the water of the lake is negligible.

Answer 1

Net force on boat = F1 + F2

Angle between F1 and F2 is 30 degrees

Magnitude of F1 = 400 N

Magnitude of F2 = 300 N

So magnitude of net force =

( (400²) +(300²) +(2 × 300 × 400 × cos(30)))^0.5

= 676.64 N

Direction = 12.81 degree east of north

Acceleration = F/m = 1.35 m/s²

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