Final answer:
To calculate the deceleration of a snowboarder going up a slope, the gravitational force component along the slope and the kinetic friction force are considered. These are used in Newton's second law to find the deceleration, which is affected by the angle of the slope and the coefficient of friction.
Step-by-step explanation:
The problem requires calculating the deceleration of a snowboarder moving up a slope with a given angle and coefficient of friction. To find the deceleration, we apply Newton's second law along the slope. The forces acting on the snowboarder are gravity, friction, and the normal force.
The gravitational force component along the slope is mg sin θ, where m is the mass of the snowboarder, g is the acceleration due to gravity, and θ is the angle of the slope. The friction force is μk mg cos θ, with μk as the kinetic friction coefficient. The deceleration a is given by (μk mg cos θ - mg sin θ) / m. This simplifies to g(μk cos θ - sin θ), as the mass m cancels out.
Putting the values into the equation, with μk = 0.10, g = 9.8 m/s2, and θ = 3.5°, we calculate the deceleration of the snowboarder. Note that the angle must be converted into radians when using trigonometric functions in the calculation. The computed deceleration must match one of the given options. Considering the specifics of the problem, such as the angle of the slope and the coefficient of friction, are vital to arrive at the correct deceleration value.