A boat has a mass of 6800 kg. Its engines generate a drive force of 4500 N, due west, while the wind exerts a force of 660 N, due east, and the water exerts a resistive force of 1200 N due east. What is the magnitude and direction of the boat's acceleration?
ma=ΣF= F(eng) –F(wind)-F9water) = >
a=(4500-660-1200)/6800 =0.388 m/s²
To find the magnitude and direction of the boat's acceleration, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's find the net force acting on the boat. The drive force and the wind force are acting in opposite directions, so we need to subtract the magnitude of the wind force from the magnitude of the drive force:
Net force = Drive force - Wind force
Net force = 4500 N - 660 N
Net force = 3840 N
Next, we need to take into account the resistive force exerted by the water, which is also acting in the opposite direction. Since the boat is moving in a straight line, the resistive force can be considered as opposing the net force acting on the boat. So, we need to subtract the magnitude of the resistive force from the net force:
Net force = Net force - Resistive force
Net force = 3840 N - 1200 N
Net force = 2640 N
Now, let's calculate the acceleration of the boat using Newton's second law. Rearranging the formula, we have:
Acceleration = Net force / Mass
Acceleration = 2640 N / 6800 kg
Acceleration ≈ 0.388 m/s^2 (rounded to three decimal places)
The magnitude of the boat's acceleration is approximately 0.388 m/s^2.
To determine the direction of the acceleration, we need to consider that the drive force and wind force are in opposite directions, while the resistive force is in the same direction as the wind force. Thus, the net force is in the direction of the drive force. Therefore, the direction of the boat's acceleration is west.
In summary, the magnitude of the boat's acceleration is approximately 0.388 m/s^2, and its direction is west.