if you were on a 22.7 degree slope and an avalanche started 425 m up the slope, how much time would you have to get out of the way, there is no friction.
To calculate the time you would have to get out of the way of an avalanche on a 22.7 degree slope, we can use basic principles of physics.
First, we need to determine the acceleration of the avalanche. Since there is no friction mentioned, we can assume the avalanche is a result of gravity acting on it. The downward force due to gravity can be broken down into two components: one parallel to the slope (mg sinθ) and one perpendicular to the slope (mg cosθ). In this case, the component parallel to the slope is what causes the acceleration. The equation for acceleration is given by a = g sinθ, where g is the acceleration due to gravity (9.8 m/s^2).
Using the given slope angle θ of 22.7 degrees, we can find the acceleration as follows:
a = 9.8 m/s^2 * sin(22.7°)
a ≈ 3.89 m/s^2
Next, we need to determine the time it takes for the avalanche to travel 425 m down the slope. To find this, we can use the kinematic equation:
s = ut + 0.5at^2
where s is the displacement (425 m), u is the initial velocity (which we assume to be 0 m/s in this case), a is the acceleration (3.89 m/s^2), and t is the time.
Rearranging the equation to solve for t, we have:
t = sqrt(2s / a)
Substituting the values, we get:
t = sqrt(2 * 425 m / 3.89 m/s^2)
t ≈ sqrt(218.65 s^2/m)
t ≈ 14.8 s
Therefore, you would have approximately 14.8 seconds to get out of the way of the avalanche on a 22.7-degree slope, assuming there is no friction.