The y-component of the acceleration is [tex]0.33 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:
[tex]u_y = u sin \theta_1 = (2.25 m/s)(sin 50.0^{\circ})=1.72 m/s[/tex]
where
u = 2.25 m/s is the initial velocity
[tex]\theta_1 = 50.0^{\circ}[/tex] is the initial direction
[tex]v_y = v sin \theta_2 = (4.65)(sin 120^{\circ})=4.03 m/s[/tex], where
v = 4.65 m/s is the final velocity
[tex]\theta_2 = 120.0^{\circ}[/tex] is the final direction
The time elapsed is
t = 8.33 s
Therefore, we can find the y-component of the acceleration:
[tex]a_y=\frac{4.03-1.72}{8.33}=0.33 m/s^2[/tex]
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