A novice skier, starting from rest, slides down a frictionless 35.0 degrees incline whose vertical height is 140 m.
1. How fast is she going when she reaches the bottom?
To find the speed of the skier at the bottom of the incline, we can use the principles of conservation of energy.
The initial energy of the skier is purely potential energy at the top of the incline, which can be calculated using the equation:
Potential Energy = m * g * h
Where:
m = mass of the skier
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = vertical height of the incline (140 m in this case)
The final energy of the skier at the bottom of the incline is the sum of potential energy and kinetic energy:
Final Energy = Potential Energy + Kinetic Energy
Assuming no energy losses due to friction or air resistance, the total energy will remain constant. Therefore, the initial potential energy will be equal to the final kinetic energy:
Potential Energy = Kinetic Energy
We can set up the equation by equating the two energies:
m * g * h = (1/2) * m * v^2
Where:
v = velocity of the skier at the bottom
By simplifying and solving for v, we find:
v = sqrt(2 * g * h * sin(theta))
Where:
theta = angle of the incline (35 degrees in this case)
Now, let's plug in the values into the equation to find the velocity:
v = sqrt(2 * 9.8 m/s^2 * 140 m * sin(35 degrees))
v ≈ 39.46 m/s
Therefore, the skier will be going approximately 39.46 m/s when she reaches the bottom of the incline.
The Force component of gravity going downhill is mgSinTheta
Vf^2=Vi^2 + 2ad where a=-mgSinTheta/m
d=-140m