The acceleration of the snowboarder is [tex]5.6 m/s^2[/tex] down along the incline
Explanation:
To find the acceleration of the snowboard, we have to analyze the forces acting along the direction parallel to the incline.
There is only one force acting in this direction, and it is the component of the weight parallel to the incline, given by
[tex]mg sin \theta[/tex]
where
m = 75.0 kg is the mass of the man
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
[tex]\theta=35^{\circ}[/tex] is the angle of the incline
Substituting, we find that the net force along the incline is:
[tex]F=(75.0)(9.8)(sin 35^{\circ})=421.6 N[/tex]
According to Newton's second law, the net force on the snowboard is equal to the product between his mass and his acceleration:
[tex]F=ma[/tex]
where a is the acceleration. Therefore, solving for a, we find
[tex]a=\frac{F}{m}=\frac{421.6}{75}=5.6 m/s^2[/tex]
And the direction of this acceleration is down along the incline.
Learn more about acceleration and Newton's second law:
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