A boat has a mass of 4010 kg. Its engines generate a drive force of 3580 N due west, while the wind exerts a force of 660 N due east and the water exerts a resistive force of 1470 N due east. Take west to be the positive direction. What is the boat's acceleration, with correct sign?
Fn = 3580 - 660 - 1470 = 1450 N. = Net
force.
a = Fn/m = 1450 / 4110 = 0.362 m/s^2.
To find the boat's acceleration, we need to apply Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. The net force is the vector sum of all the forces acting on the object. In this case, we have three forces acting on the boat: the drive force, the wind force, and the water resistive force.
The drive force points west and has a magnitude of 3580 N. Since west is considered the positive direction, this force can be written as +3580 N.
The wind force points east and has a magnitude of 660 N. However, since we take west to be the positive direction, we need to consider this force as -660 N.
Similarly, the water resistive force also points east and has a magnitude of 1470 N. So, we write this force as -1470 N.
Now, let's calculate the net force:
Net force = Drive force + Wind force + Water resistive force
= +3580 N + (-660 N) + (-1470 N)
= 3580 N - 660 N - 1470 N
Simplifying the equation gives us:
Net force = 1450 N
Next, we can use Newton's second law to find the boat's acceleration. Rearranging the equation, we have:
Net force = Mass x Acceleration
Substituting the values,
1450 N = 4010 kg x Acceleration
Now, we can solve for acceleration:
Acceleration = 1450 N / 4010 kg
= 0.3611 m/s²
Therefore, the boat's acceleration, with the correct sign, is 0.3611 m/s² in the positive direction, which means it's accelerating westward.