Final answer:
The correct formula to calculate the acceleration opposite to the snowboarder's uphill motion on a 5.00° slope is a = g sin(θ) + μk cos(θ), accounting for gravity and kinetic friction.
Step-by-step explanation:
To calculate the acceleration opposite to the motion of a snowboarder going up a 5.00° slope, we must account for both the gravitational component along the slope and the frictional force. The acceleration due to gravity along the slope is g sin(θ), where g is the acceleration due to gravity and θ is the angle of the incline.
The frictional force can be represented as μk mg cos(θ), where μk is the coefficient of kinetic friction. In this case, the snowboarder is going uphill, so the acceleration due to the component of gravity is in the opposite direction to the motion and adds to the deceleration caused by friction.
Therefore, the total acceleration opposite to the motion is the sum of the gravitational component (downhill) and the frictional force (uphill). The correct formula to use would be: a = g sin(θ) + μk cos(θ), which matches option (a) in the student's set of possible answers. This combines both the gravitational deceleration and the deceleration due to friction.