A boat has a mass of 1800 kg Its engines generate a drive fo

A boat has a mass of 1800 kg. Its engines generate a drive force of 4650N due East, while the wind exerts a force of 730N due West, and the water current pushes the boat North with a force of 1200 N. What is the magnitude and direction of the boat\'s acceleration?

Solution

We need to find the direction of the net force and then that direction would be same as that of the acceleration.

We wil find the net force along the x and Y direction and then find the resultant force.

Force along the X direction = 4650 - 730 = 3920 N

Force along the Y direction = 1200 N

Net force = sqrt(Fx² + Fy²) = 4099.56 N

Hence the net acceleration = Force / Mass = 2.278 m/s²

Also the for the angle the net force would make with the x axis we have:

tan = Fy / Fx

or, = 17.0

Therefore the net acceleration is 2.278 m/s² at an angle of 17 degrees north of east.