The x-component of the acceleration is [tex]-0.45 m/s^2[/tex]
Explanation:
In order to find the x-component of the acceleration, we just need to analyze the motion in the x-direction.
The acceleration along the x-direction is given by:
[tex]a_x = \frac{v_x-u_x}{t}[/tex]
where
[tex]v_x[/tex] is the final velocity in the x-direction
[tex]u_x[/tex] is the initial velocity in the x-direction
t is the time
At the beginning, the ice skater is moving at
u = 2.25 m/s
in a direction
[tex]\theta=50.0^{\circ}[/tex]
So the initial velocity in the x-direction is
[tex]u_x = u cos \theta = (2.25)(cos 50.0)=1.45 m/s[/tex]
After t = 8.33 s, the ice skater is moving at
v = 4.65 m/s
in a direction
[tex]\theta=120^{\circ}[/tex]
So the final velocity in the x-direction is
[tex]v_x = vcos \theta=(4.65)(cos 120)=-2.33 m/s[/tex]
Therefore, the x-component of the acceleration is:
[tex]a_x = \frac{-2.33 - 1.45}{8.33}=-0.45 m/s^2[/tex]
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