A sight seen on many bunny hills across Ontario is young skiers pushing on ski poles and gliding down a slope until they come to rest. Observing from a distance, you note a young person (approximately 25 kg) pushing off with the ski poles to give herself an initial velocity of 3.5 m/s. If the inclination of the hill is 5.0 degrees and the coefficient of kinetic friction for the skis on dry snow is 0.20, calculate
a) the time taken for the skier to come to a stop
b) the distance travelled down the hill
To calculate the time taken for the skier to come to a stop and the distance traveled down the hill, we will need to use the principles of forces and motion.
First, let's determine the force acting on the skier as she glides down the hill. The only force acting on the skier in the downhill direction is the component of her weight parallel to the slope. We can calculate this force using the equation:
Force downhill = weight x sin(angle of inclination)
Weight = mass x gravity
Given that the mass of the skier is 25 kg and the angle of inclination is 5.0 degrees, we have:
Weight = 25 kg x 9.8 m/s^2 = 245 N
Force downhill = 245 N x sin(5.0 degrees)
Next, let's determine the force of friction opposing the skier's motion. The force of friction is given by the equation:
Force of friction = coefficient of friction x normal force
The normal force is equal to the weight of the skier, so we have:
Force of friction = 0.20 x 245 N
Now, we can calculate the net force acting on the skier by subtracting the force of friction from the force downhill:
Net force = Force downhill - Force of friction
Having calculated the net force, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
Net force = mass x acceleration
Rearranging this equation, we can solve for acceleration:
Acceleration = Net force / mass
Given that the mass of the skier is 25 kg, we can calculate the acceleration.