A rugby player runs with the ball directly toward his opponent's goal, along the positive direction of an x axis. He can legally pass the ball to a teammate as long as the ball's velocity relative to the field does not have a positive x component. Suppose the player runs at speed 3.5 m/s relative to the field while he passes the ball with velocity `vecv_(BP)` relative to himself. If `vecv_(BP)` has magnitude 6.0m/s, what is the smallest angle it can have for the pass to be legal?

Explanation

To solve the problem, we need to find the smallest angle at which the rugby player can pass the ball while ensuring that the ball's velocity relative to the field does not have a positive x-component. Let's break down the solution step by step.

### Step 1: Understand the velocities involved
The rugby player runs with a velocity \( \vec{v}_{P} = 3.5 \, \text{m/s} \) in the positive x-direction. When he passes the ball, the ball has a velocity \( \vec{v}_{BP} \) relative to the player, with a magnitude of \( 6.0 \, \text{m/s} \).

### Step 2: Set up the components of the ball's velocity
The velocity of the ball relative to the player can be expressed in terms of its components:
\[
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