The board's displacement during the acceleration time after the sailboard was hit by the gust is 32.9 m.
The magnitude of the board's displacement can be calculated with the following equation:
[tex]x_{f} = x_{i} + v_{i}t + \frac{1}{2}at^{2}[/tex]
Where:
[tex] x_{f} [/tex]: is the final displacement =?
[tex] x_{i} [/tex]: is the initial displacement = 0
[tex]v_{i}[/tex]: is the initial velocity
t: is the time = 5.42 s
a: is the acceleration = 0.714 m/s²
Since the hits the sailboard at 48.8° from the original direction, the initial velocity is:
[tex]v_{i} = v*cos(\theta) = 6.28 m/s*cos(48.8) = 4.14 m/s[/tex]
Hence, the displacement is:
[tex]x_{f} = v_{i}t + \frac{1}{2}at^{2} = 4.14 m/s*5.42 s + \frac{1}{2}0.714 m/s^{2}*(5.42 s)^{2} = 32.9 m[/tex]
Therefore, the magnitude of the board's displacement is 32.9 m.
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