Two people are pulling a boat through the water as in the figure below. Each exerts a force of 600 N directed at a è = 20.0° angle relative to the forward motion of the boat. If the boat moves with constant velocity, find the resistive force exerted by the water on the boat.
Since the boat is moving at constant velocity, the net force on the boat along the direction of motion must be zero.
That means the resistive force is equal and opposite to the sum of the forward components of the two towing forces.
To find the resistive force exerted by the water on the boat, we need to resolve the 600 N force into its horizontal and vertical components.
The horizontal component of the force is given by:
F_horizontal = F * cos(è)
where F = 600 N and è = 20.0°.
F_horizontal = 600 N * cos(20.0°)
F_horizontal ≈ 557.37 N (rounded to two decimal places)
The vertical component of the force is given by:
F_vertical = F * sin(è)
where F = 600 N and è = 20.0°.
F_vertical = 600 N * sin(20.0°)
F_vertical ≈ 203.92 N (rounded to two decimal places)
Since the boat is moving with constant velocity, the resistive force exerted by the water on the boat is equal in magnitude and opposite in direction to the sum of the horizontal forces.
Therefore, the resistive force exerted by the water on the boat is approximately 557.37 N in the opposite direction of motion.
To find the resistive force exerted by the water on the boat, we can use the concept of vector addition.
The force exerted by each person can be represented as a vector. Let's call the force exerted by person 1 as F1 and the force exerted by person 2 as F2.
Given:
Force exerted by each person (F1 and F2) = 600 N
Angle between the force and the forward motion of the boat (θ) = 20.0°
To find the resistive force, we need to find the net force acting on the boat. This can be done by adding the individual forces using vector addition.
Step 1: Resolve the forces into their horizontal and vertical components.
The horizontal components of the forces can be found using the equation:
F_horizontal = F * cos(θ), where F is the magnitude of the force and θ is the angle.
F1_horizontal = F1 * cos(θ) = 600 N * cos(20.0°)
F2_horizontal = F2 * cos(θ) = 600 N * cos(20.0°)
Step 2: Find the net force in the horizontal direction.
Since the boat is moving with constant velocity, the net force in the horizontal direction should be zero.
Net force_horizontal = F1_horizontal + F2_horizontal = 0
Step 3: Find the vertical components of the forces.
The vertical components of the forces can be found using the equation:
F_vertical = F * sin(θ), where F is the magnitude of the force and θ is the angle.
F1_vertical = F1 * sin(θ) = 600 N * sin(20.0°)
F2_vertical = F2 * sin(θ) = 600 N * sin(20.0°)
Step 4: Find the net force in the vertical direction.
The net force in the vertical direction is equal to the resistive force exerted by the water on the boat.
Net force_vertical = F1_vertical + F2_vertical = Resistive force
Resistive force = F1_vertical + F2_vertical = 600 N * sin(20.0°) + 600 N * sin(20.0°)
Now you can calculate the value of the resistive force using this equation.