Starting from rest, a 75.0-kg snowboarder slides straight down a 115-m slope in 6.6 seconds. If the slope is a 35° incline, find the following:

(a) The acceleration of the snowboarder.

Question

Middle School

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Answer :

skyluke89 skyluke89 · Answer 1 · 2024-11-16T23:05:56-05:00

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.

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