A skier slides down a ski slope with an acceleration 2.2 m/s^2 directed down the slope. The coefficient of kinetic friction between the skis and the slope is 0.24. What is the angle of the slope �with the ground?
friction force up slope = .24 m g cos A
gravity down slope = m g sin A
m (2.2) = m (9.81)(sin A - .24 cos A)
sin A - .24 cos A = .224
well I can make a table
A, left side
0, -.24
5, .083
10, .17
15, .254
so between 10 and 15 deg
13, .22
13 degrees is very close
try 13.2
13.2 , .224 close enough
To find the angle of the slope with the ground, we can use the information given about the acceleration and the coefficient of kinetic friction.
The acceleration of the skier down the slope is given as 2.2 m/s^2 directed down the slope. We can break this acceleration into two components: one parallel to the slope and one perpendicular to the slope.
Let's assume that the angle of the slope with the ground is θ. The component of acceleration parallel to the slope is given by a_parallel = a * sinθ, and the component perpendicular to the slope is given by a_perpendicular = a * cosθ.
The skier experiences a kinetic friction force opposing its motion down the slope, which can be calculated using the coefficient of kinetic friction and the normal force. The normal force is equal to the gravitational force acting on the skier, which is equal to the skier's mass multiplied by the acceleration due to gravity (9.8 m/s^2).
The kinetic friction force (F_f) is given by F_f = μ * N, where μ is the coefficient of kinetic friction and N is the normal force. Therefore, F_f = μ * m * g, where m is the mass of the skier.
Since the skier experiences a net force, we can find the net force by using Newton's second law of motion: F_net = m * a. In this case, the net force is equal to the force parallel to the slope minus the kinetic friction force: F_net = m * a_parallel - μ * m * g.
From the previous step, we can find a_parallel as a_parallel = a * sinθ. Therefore, F_net = m * a * sinθ - μ * m * g.
Since F_net = m * a, we can solve for sinθ: a * sinθ - μ * m * g = a.
Rearranging the equation, we have sinθ = (a + μ * m * g) / a.
Now we can substitute the given values into the equation: sinθ = (2.2 + 0.24 * m * 9.8) / 2.2.
Finally, we can solve for θ by taking the inverse sine (arcsin) of both sides of the equation: θ = arcsin((2.2 + 0.24 * m * 9.8) / 2.2).
To find the angle of the slope with the ground, you would need to know the mass of the skier and substitute it into the equation above.