Question

The figure shows two kayakers pulling a raft. One kayaker pulls with force vector F sub 1 equals open angled bracket 190 comma 160 close angled bracket comma and the other kayaker pulls with force vector F sub 2 equals open angled bracket 128 comma negative 121 close angled bracket period

two vectors F sub 1 and F sub 2 that share an initial point located on a raft, F sub 1 points right and up where its terminal point is at a kayak, F sub 2 points left and down where its terminal point is at another kayak

What is the angle between the kayakers? Round your answer to the nearest degree. (2 points)
78°
83°
86°
80°

Answer 1

Answer: Therefore, the angle between the kayakers is approximately 63 degrees. The closest answer choice is 78°.

Explanation:

To find the angle between the kayakers, we can use the dot product formula:

F sub 1 · F sub 2 = ||F sub 1|| ||F sub 2|| cos θ

where · denotes the dot product, || || denotes the magnitude, and θ is the angle between the two vectors.

First, we need to find the magnitudes of F sub 1 and F sub 2:

||F sub 1|| = sqrt(190^2 + 160^2) = 247.79

||F sub 2|| = sqrt(128^2 + (-121)^2) = 170.10

Next, we need to find the dot product of F sub 1 and F sub 2:

F sub 1 · F sub 2 = (190)(128) + (160)(-121) = -12080

Substituting these values into the dot product formula, we get:

-12080 = (247.79)(170.10) cos θ

Solving for cos θ, we get:

cos θ = -0.424

Taking the inverse cosine of both sides, we get:

θ ≈ 116.8°

However, this is the angle between the two vectors in standard position (i.e., with initial points at the origin). To find the angle between the kayakers, we need to subtract this angle from 180°:

180° - θ ≈ 63.2°