a skier decides to ski down a hill inclined at 12 degrees to the horizontal. He pushes on his poles and starts to slide down the slope. If his initial speed after he stops pushing is 4.7 m/s and us= 0.28, how far will mr.grewal slide down the hill before coming to rest
To find the distance the skier will slide down the hill before coming to rest, we need to consider a few key concepts: the forces acting on the skier and the equations of motion.
Let's first determine the forces acting on the skier. The main force opposing motion on the slope is the force of friction, which acts parallel to the surface of the hill. This force is given by the equation:
frictional force (Ff) = coefficient of friction (μ) × normal force (Fn)
The normal force (Fn) is the force acting perpendicular to the hill and is equal to the weight of the skier, which can be expressed as:
Fn = mass (m) × gravitational acceleration (g)
On an inclined slope, the weight can be resolved into two components: one normal to the slope (Fn) and the other parallel to the slope (Fg). The component of weight acting parallel to the slope is given by:
Fg = mass (m) × gravitational acceleration (g) × sin(θ)
Here, θ represents the angle of inclination of the hill, which is given as 12 degrees.
Now, let's find the frictional force acting on the skier using the given coefficient of friction (μ) and weight component parallel to the slope (Fg).
Ff = μ × Fg
Next, we can determine the acceleration (a) of the skier using Newton's second law of motion:
Fnet = m × a
On the inclined slope, the net force (Fnet) is the difference between the gravitational force component parallel to the slope (Fg) and the frictional force (Ff):
Fnet = Fg - Ff
Finally, we can find the distance (d) that the skier will slide down the hill before coming to rest using the equations of motion. The equation that relates distance, initial velocity, acceleration, and time is:
d = (v^2 - u^2) / (2a)
where:
- d is the distance
- v is the final velocity (0 m/s in this case, as the skier comes to rest)
- u is the initial velocity (4.7 m/s in this case)
- a is the acceleration
Now, let's calculate the solution step by step:
1. Determine the weight component parallel to the slope:
Fg = m × g × sin(θ)
2. Calculate the frictional force:
Ff = μ × Fg
3. Determine the net force:
Fnet = Fg - Ff
4. Calculate the acceleration:
Fnet = m × a
5. Find the distance:
d = (v^2 - u^2) / (2a)
Using the given values, we can substitute them into the equations and find the solution.