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A boat of mass 211.0 kg is moving due north at a speed of 15.9 m/s. A crosswind blowing east exerts a force of 37.6 N. After 45.7 seconds, what is the angle of the boat's trajectory measured from the north?

Answer :

The angle of the boat's trajectory, as measured off of north, is approximately 86.7 degrees.

To find the angle of the boat's trajectory, we can use trigonometry. The boat's motion is a result of the combined effect of its northward velocity and the eastward force exerted by the crosswind.

Given:

Mass of the boat (m) = 211.0 kg

Velocity of the boat (v) = 15.9 m/s

Force exerted by the crosswind (F) = 37.6 N

Time (t) = 45.7 s

First, we calculate the acceleration of the boat using Newton's second law:

F = ma

Rearranging the equation, we get:

a = F / m

a = 37.6 N / 211.0 kg

a ≈ 0.1782 m/s²

Next, we calculate the displacement of the boat in the eastward direction using the equation of motion:

d = 0.5 * a * t²

d = 0.5 * 0.1782 m/s² * (45.7 s)²

d ≈ 232.0 m

Now, we can calculate the angle of the boat's trajectory (θ) using the tangent function:

tan(θ) = d / v

θ = arctan(d / v)

θ = arctan(232.0 m / 15.9 m/s)

Using a calculator, we find:

θ ≈ 86.7 degrees

Therefore, the angle of the boat's trajectory, as measured off of north, is approximately 86.7 degrees.

To learn more about, trigonometry, click here, https://brainly.com/question/29002217

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