The wind exerts a force of 284 N North on
a sailboat, while the water exerts a force of
132 N West on the sailboat.
What is the magnitude of the net external
force on the sailboat?
Answer in units of N
Fn = sqrt((x^2 + y^2),
Fn = sqrt((-132)^2 + (284)^2) = 313.2N.
To find the magnitude of the net external force on the sailboat, we need to calculate the resultant force by considering both the wind force and water force.
Given:
Wind force = 284 N North
Water force = 132 N West
We can represent the forces on a coordinate system, where North is the positive y-axis and West is the negative x-axis.
The wind force of 284 N North can be represented as (+0 N, +284 N) and the water force of 132 N West can be represented as (-132 N, +0 N).
To find the net external force, we need to add these two vectors together.
Adding the x-components: -132 N + 0 N = -132 N
Adding the y-components: 0 N + 284 N = 284 N
So, the vector sum of these forces is (-132 N, +284 N).
To find the magnitude of the net external force, we can use the Pythagorean theorem:
Magnitude = sqrt((-132 N)^2 + (284 N)^2)
Magnitude = sqrt(17424 + 80656)
Magnitude = sqrt(98080)
Magnitude ≈ 313.192 N
Therefore, the magnitude of the net external force on the sailboat is approximately 313.192 N.