A novice skier, starting from rest, slides down a frictionless 35.0 degree incline whose vertical height is 140 m.
1. How fast is she going when she reaches the bottom?
To determine the speed of the skier when she reaches the bottom of the incline, you can use the principles of conservation of energy.
First, we need to calculate the gravitational potential energy (PE) of the skier at the top of the incline and convert it into kinetic energy (KE) at the bottom of the incline.
The potential energy at the top is given by the equation:
PE = m * g * h
where m is the mass of the skier, g is the acceleration due to gravity (9.8 m/s²), and h is the vertical height of the incline (140 m).
To convert the potential energy into kinetic energy, we use the equation:
PE = KE
m * g * h = (1/2) * m * v²
where v is the velocity of the skier at the bottom.
Simplifying the equation, we get:
v² = (2 * g * h)
v = √(2 * g * h)
Substituting the given values:
v = √(2 * 9.8 * 140) m/s
v ≈ 52.3 m/s
Therefore, the skier will be going approximately 52.3 m/s when she reaches the bottom of the incline.