A boat pulled through a canal by horses walking parallel to the canal and exerting a force of 1000 N on a tow Rope 40 meters long. Is the distance from the boat to the horse track is 15 meters, what is the magnitude of the effective component pulling the boat forward
1000 cosθ
where sinθ = 15/40
1000cos[ sin^-1 (15/40) ]
or
1000 [ sqrt(1600-225)]/40
To find the effective component pulling the boat forward, we can use the concept of vectors and trigonometry. The effective component will be the horizontal component of the force exerted by the horses.
The force exerted by the horses is 1000 N, and the distance from the horse track to the boat is 15 meters. This distance is the perpendicular distance from the horse track to the tow rope.
To find the effective component, we need to calculate the angle between the force vector and the perpendicular distance. This angle can be found using trigonometry.
Let's call the angle between the force vector and the perpendicular distance as theta.
sin(theta) = perpendicular distance / length of the tow rope
sin(theta) = 15 / 40
theta = sin^(-1)(15 / 40)
Now, let's calculate the value of theta:
theta = sin^(-1)(0.375)
theta ≈ 22.62 degrees
The horizontal component can be found by taking the cosine of theta and multiplying it by the force exerted by the horses.
horizontal component = force exerted by the horses * cos(theta)
horizontal component = 1000 N * cos(22.62)
Now, let's calculate the value of the horizontal component:
horizontal component ≈ 1000 N * 0.923
horizontal component ≈ 923 N
Therefore, the magnitude of the effective component pulling the boat forward is approximately 923 N.
To find the magnitude of the effective component pulling the boat forward, we can use trigonometry.
Let's consider the diagram of the scenario described:
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O (Boat)
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h
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(Horse Track)
In this diagram, the distance from the boat to the horse track is represented as "h."
We can consider the effective component pulling the boat forward as the horizontal component of the force exerted by the horses on the tow rope.
From the given information, we know that the force exerted by the horses is 1000 N. The length of the tow rope is 40 meters.
To find the magnitude of the effective component pulling the boat forward, we can use the right triangle formed by the tow rope, the horse track, and the effective force.
Using the Pythagorean theorem, we have:
(Effective Force)^2 = (Force exerted by the horses)^2 - (Vertical Component)^2
The vertical component can be calculated as h, the distance from the boat to the horse track.
Therefore:
(Effective Force)^2 = (1000 N)^2 - h^2
To solve for the effective component pulling the boat forward, we take the square root of both sides:
Effective Force = sqrt((1000 N)^2 - h^2)
Substituting the given value of h = 15 meters:
Effective Force = sqrt((1000 N)^2 - (15 m)^2)
Simplifying this expression will give you the magnitude of the effective component pulling the boat forward.