Answer: 10.39 m/s.
Explanation: This is a physics problem that involves vector components and trigonometry. To solve it, we need to find the angle between the pine cone’s impact velocity and the ground, and then use the cosine function to find the component parallel to the ground. Here are the steps:
First, we draw a diagram of the situation, as shown below. We label the pine cone’s impact velocity as v → v , the angle between v → v and the vertical as θ \theta , and the angle between the ground and the horizontal as 30 ∘ 30^{\circ} .
Next, we use the fact that the sum of the angles in a triangle is 180 ∘ 180^{\circ} to find θ \theta . We have θ + 30 ∘ + 90 ∘ = 180 ∘ \theta + 30^{\circ} + 90^{\circ} = 180^{\circ} , so θ = 60 ∘ \theta = 60^{\circ} .
Then, we use the cosine function to find the component of v → v parallel to the ground, which we call v x v_x . We have v x = v cos ( θ − 30 ∘ ) v_x = v \cos (\theta - 30^{\circ}) , where v v is the magnitude of v → v , which is given as 12 m/s. Plugging in the values, we get v x = 12 cos ( 60 ∘ − 30 ∘ ) = 12 cos ( 30 ∘ ) = 12 × 0.866 = 10.39 m/s v_x = 12 \cos (60^{\circ} - 30^{\circ}) = 12 \cos (30^{\circ}) = 12 \times 0.866 = 10.39 \text{ m/s}
Finally, we round our answer to two decimal places and write it in a sentence. The component of the pine cone’s impact velocity parallel to the ground is 10.39 m/s.