A boat has a mass of 5680 kg. Its engines generate a drive force of 3380 N due west, while the wind exerts a force of 990 N due east and the water exerts a resistive force of 1310 N due east. Take west to be the positive direction. What is the boat's acceleration, with correct sign?
F = ma
just add up the vectors, after dividing by the mass.
To find the boat's acceleration, we need to use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
In this case, the net force acting on the boat is the vector sum of all the forces. We can calculate the net force by subtracting the forces in the opposite direction from the forces in the positive direction.
The positive force in this case is the drive force generated by the engines, which is 3380 N due west. The negative forces are the wind force and water resistance force, both of which are acting due east.
So, the net force can be calculated as follows:
Net force = (drive force) - (wind force) - (water resistance force)
Net force = 3380 N - 990 N - 1310 N
Net force = 3380 N - 2300 N
Net force = 1080 N due west
Now, we can use Newton's second law to calculate the boat's acceleration:
Acceleration = Net force / Mass
Acceleration = 1080 N / 5680 kg
Calculating this, we find:
Acceleration = 0.19 m/s² due west
Therefore, the boat's acceleration, with the correct sign, is 0.19 m/s² due west.