The y-component of the acceleration is [tex]0.22 m/s^2[/tex]
Explanation:
The y-component of the acceleration is given by
[tex]a_y = \frac{v_y-u_y}{t}[/tex]
where
[tex]v_y[/tex] is the y-component of the final velocity
[tex]u_y[/tex] is the y-component of the initial velocity
t is the time elapsed
For the ice skater in this problem, we have:
u = 2.25 m/s is the initial velocity, in a direction [tex]\theta=50.0^{\circ}[/tex]
v = 4.65 m/s is the final velocity, in a direction [tex]120^{\circ}[/tex]
t = 8.33 s is the time elapsed
The y-components of the initial and final velocity are:
[tex]u_y = u sin \theta = (2.25)(sin 50^{\circ})=1.72 m/s\\v_y = v sin \theta = (4.65)(sin 50^{\circ})=3.56 m/s[/tex]
So the y-component of the acceleration is
[tex]a_y = \frac{3.56-1.72}{8.33}=0.22 m/s^2[/tex]
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