In the figure, particle A moves along the line y = 29 m with a constant velocity of magnitude 3.5 m/s and parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and constant acceleration of magnitude 0.44 m/s2. What angle θ between and the positive direction of the y axis would result in a collision?

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To determine the angle θ that would result in a collision between particle A and particle B, we need to find the time it takes for particle B to reach the y-coordinate of particle A.

Let's break down the problem step by step:

1. Find the time it takes for particle A to pass the y-axis:
- Since particle A has a velocity of 3.5 m/s, we can use the equation of motion: velocity = displacement/time.
- The displacement is the distance from the y-axis to the starting position of particle A, which is 29 m.
- The time it takes for particle A to reach the y-axis can be found by rearranging the equation: time = displacement/velocity.

time_A = 29 m / 3.5 m/s

2. Find the position of particle B at this time:
- Particle B starts at the origin (0, 0) and has a constant acceleration of 0.44 m/s^2.
- The position of particle B can be determined using the equation of motion: position = initial position + initial velocity * time + (1/2) * acceleration * time^2.
- Since particle B starts with zero initial velocity, the equation simplifies to: position = (1/2) * acceleration * time^2.

position_B = (1/2) * (0.44 m/s^2) * (time_A)^2

3. Find the angle θ:
- The angle θ is the angle between the positive direction of the y-axis and the line connecting the origin to the position of particle B.
- We can use trigonometry to find this angle by calculating the tangent of θ: tan(θ) = position_B / (horizontal distance to position B).

θ = atan(position_B / (horizontal distance to position B))

- The horizontal distance to position B is the same as the magnitude of particle A's velocity multiplied by the time it took to reach the y-axis.

horizontal distance to position B = |velocity_A| * time_A

We can now plug in the values and solve for the angle θ.