To find the length of the hill for a skier descending with constant friction, calculate the skier's acceleration using Newton's second law to consider both gravity and friction, and then apply kinematic equations with the given time of descent.
To calculate the length of the hill a 60.0 kg skier descends, we first need to determine the acceleration of the skier given the slope and the frictional force acting against the skier's motion. We can apply Newton's second law which states that F = ma, where F is the net force acting on an object, m is its mass, and a is its acceleration.
Since the skier is on a 30.0° slope, the component of gravitational force along the slope is mg sin(30.0°), where g is the acceleration due to gravity (approximately 9.81 m/s2). The friction force acts in the opposite direction, and thus the net force is mg sin(30.0°) - 72.0 N.
Substituting in the values and solving for acceleration a, we have:
a = (60.0 kg * 9.81 m/s2 * sin(30.0°) - 72.0 N) / 60.0 kg
Once we have the acceleration, we can use kinematic equations to find the length of the hill. For an object starting from rest and moving with constant acceleration, the distance d is given by
d = 0.5 * a * t2
where t is the time taken to travel the distance, which is 4.00 s in this case. Substituting the found value of a into this equation will give us the length of the hill.