Question

You drive a 6,000 kg boat due north, while the wind exerts a force of 600 N due south and the water exerts a resistive force of 1,200 N due south. The generated force by the boat’s engines is 4,200 N. Find the magnitude and direction of the boat’s acceleration.

Answer 1

According to Newton's second law of motion, net force is equal to the product of mass and acceleration.


`F_(net) =(mass)(acceleration)`

Since what we are looking for is acceleration, we need to tweak our formula to derive our formula for acceleration.


`acceleration = F_(net)/mass`

Our only problem is we do not have the value of the net force yet, but we can do so with the given presented.

Let's first wake into account all the forces acting upon the object.

F1 = 600N South
F2 = 1,200 N South
F3 - 4,200 N North

Net Force is the sum of all forces acting on an object. But you need to take into account that the forces are not all going towards the same direction. In this case, there are forces that are going against each other.

Thinking about the Cartesian plane, if you count going downwards the values are negative and if you count going up, the numbers are positive. We can apply this to our scenario here.

South is negative and north is positive. Our Forces then will now be considered this way:

F1 = -600N South
F2 = -1,200N South
F3 = 4,200N North

Now we can come up with our net force.


`F_(net) = (-600N) + (-1,200N) + 4,200N`

`F_(net) = (-1,800N) + 4,200N`

`F_(net) = 2,400N`

Our net force is equal to 2,400N. It is positive so the direction is North.

Since we have our net force, we can now solve for acceleration.



`acceleration = F_(net)/mass`


`acceleration = 2,400N/6,000kg`


`acceleration = 0.40m/s^(2)`

So the boat is moving at
`0.40 m/ s^(2)` to the North.