DYNAMICS:
a skier starts at the top of a 30m hill ta an anle of 20 degrees. the skier goes straight down the firctionless slope. How long will it take the skier to get to the bottom?
The distance that he has to ski is
D = 30m/sin20 = 87.7 m
The acceleration component down the slope is g sin 20 = 3.35 m/s^2
D = (1/2)*(3.35) t^2 = 87.7 m
t^2 = 52.35 s^2
t = 7.2 seconds
To determine how long it will take for the skier to get to the bottom of the hill, we can use the principles of kinematics and dynamics.
First, let's break down the problem into its components. We have a hill with an angle of 20 degrees and a vertical distance of 30m that the skier needs to traverse. We can assume the skier's initial velocity is zero because they are starting from rest.
To solve this problem, we need to use the equations of motion. One such equation is the equation of motion for uniform acceleration in the vertical direction:
s = ut + (1/2)at^2
Where:
- s is the vertical distance traveled (30m in this case)
- u is the initial velocity (0 m/s)
- a is the acceleration due to gravity, which is approximately 9.8 m/s^2 (assuming the skier is not influenced by air resistance)
- t is the time it takes to travel the given distance
Since the skier is traveling straight down the slope, the only force acting on them is gravity, which provides the acceleration. Therefore, we can substitute the value of acceleration into the equation:
30 = 0(t) + (1/2)(9.8)(t^2)
Simplifying this equation, we get:
30 = 4.9t^2
Rearranging the equation, we have:
t^2 = 30 / 4.9
t^2 = 6.1224
Now, taking the square root of both sides, we find:
t ≈ √6.1224
t ≈ 2.47 seconds
Therefore, it will take the skier approximately 2.47 seconds to get to the bottom of the hill.