I. To find the velocity of the snowboarder at the bottom of the hill, we can use the principle of conservation of energy.
The initial potential energy (PE1) of the snowboarder at the top of the hill is converted into the final kinetic energy (KE2) at the bottom of the hill.
The initial potential energy can be given as:
PE1 = m * g * h1
where m is the mass of the snowboarder, g is the acceleration due to gravity, and h1 is the height of the hill.
The final kinetic energy can be given as:
KE2 = (1/2) * m * v^2
where v is the velocity at the bottom of the hill.
Since energy is conserved, PE1 = KE2.
Therefore, we can equate the two equations as:
m * g * h1 = (1/2) * m * v^2
Simplifying the equation, we can find the velocity (v):
v = sqrt(2 * g * h1)
Given:
- h1 = 44 m
- g ≈ 9.8 m/s^2 (acceleration due to gravity)
Plugging in the values, we can calculate the velocity at the bottom of the hill (v).
II. To find how far the snowboarder can travel up the 27° slope, we can use a similar approach and consider energy conservation.
Using the same principle of conservation of energy, we can equate the initial potential energy (PE2) on the 27° slope to the final potential energy (PE3) that the snowboarder reaches.
The initial potential energy on the 27° slope can be given as:
PE2 = m * g * h2
where h2 is the height corresponding to the 27° slope.
The final potential energy can be given as:
PE3 = m * g * h3
where h3 is the height the snowboarder reaches on the 27° slope.
Since energy is conserved, PE2 = PE3.
Therefore, we can equate the two equations as:
m * g * h2 = m * g * h3
We can cancel out the mass (m) on both sides of the equation, which gives:
h2 = h3
This means that the snowboarder can travel up the slope until the height at the 27° slope matches the height at the 15° hill.
Therefore, the distance the snowboarder can travel up the 27° slope is equal to the horizontal distance she glided before reaching the upward slope, which is given as 10 m.