A 52kg skier starts at rest and slides 30m down a hill inclined at 12 degrees relative to the horizontal. List five quantities thatbdescribe the motion of the skier and solve for of them( aleast one of them should be be a kinematic quantity).

I know these quantities
M: 52 kg
Fg:52 N
Fn: 52 n
Is distance 30 meters down hill

32

Sure! Here are five quantities that describe the motion of the skier:

1. Distance: The skier slides a distance of 30 meters down the hill.
2. Time: The time it takes for the skier to slide down the hill is unknown.
3. Velocity: The skier's initial velocity is zero since they start at rest. We can calculate their final velocity using kinematic equations.
4. Acceleration: The skier's acceleration can be calculated using the gravitational force and the angle of the incline.
5. Force: The gravitational force acting on the skier is equal to their weight, which is 52 N.

Now, let's solve for the final velocity using the kinematic equations. The most appropriate equation is:

vf^2 = vi^2 + 2ad

where:
- vf is the final velocity (which we are trying to find)
- vi is the initial velocity (zero in this case)
- a is the acceleration (which we can calculate)
- d is the distance (30 meters)

We know the equation for acceleration is:

a = g * sin(theta)

where:
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- theta is the angle of the incline (12 degrees)

Plugging in the values:

a = 9.8 m/s^2 * sin(12 degrees)
a ≈ 2.017 m/s^2

Now, we can calculate the final velocity:

vf^2 = 0 + 2 * 2.017 m/s^2 * 30 m
vf^2 ≈ 121.02 m^2/s^2

Taking the square root of both sides:

vf ≈ √121.02 m^2/s^2
vf ≈ 11 m/s

So, the final velocity of the skier after sliding 30 meters down the hill is approximately 11 m/s.

The five quantities that describe the motion of the skier are:

1. Distance (already provided): The skier slides a distance of 30 meters down the hill.

2. Time: The time it takes for the skier to slide down the hill.

3. Velocity: The velocity of the skier at any given point during the slide.

4. Acceleration: The acceleration of the skier during the slide.

5. Force: The net force acting on the skier.

Let's solve for one of these quantities, velocity:

To solve for velocity, we need to use the kinematic equation:

v^2 = u^2 + 2as

where:
v is the final velocity (unknown),
u is the initial velocity (which is zero since the skier starts from rest),
a is the acceleration (unknown),
and s is the distance (given as 30 meters).

Since the skier starts from rest, the initial velocity (u) is 0 m/s.

Let's assume the acceleration of the skier is due to gravity. The acceleration due to gravity (g) can be calculated using:

g = 9.8 m/s^2 (standard value)

The force of gravity acting on the skier is given by:

Fg = m * g
= 52 kg * 9.8 m/s^2
= 509.6 N

The component of the gravitational force parallel to the slope is:

Fparallel = Fg * sin(θ)
= 509.6 N * sin(12°)
= 105.1 N

Now, we can calculate the acceleration (a) using Newton's second law:

Fnet = m * a

Since there are no other forces acting on the skier in the horizontal direction, the net force is equal to the parallel component of the gravitational force:

Fnet = Fparallel = 105.1 N

Therefore,

105.1 N = 52 kg * a

Solving for a:

a = 105.1 N / 52 kg
= 2.02 m/s^2

Now, we can substitute these values into the kinematic equation:

v^2 = u^2 + 2as

v^2 = 0^2 + 2 * 2.02 m/s^2 * 30 m
v^2 = 120.6 m^2/s^2

Taking the square root of both sides:

v = √(120.6 m^2/s^2)
v ≈ 10.98 m/s

Therefore, the velocity of the skier is approximately 10.98 m/s.

The motion of the skier can be described by various quantities. Here are five quantities that describe the motion of the skier:

1. Distance: The skier slides a distance of 30 meters down the hill inclined at 12 degrees. (Given)

2. Time: The time it takes for the skier to slide down the hill. This can be determined using kinematic equations.

3. Acceleration: The acceleration experienced by the skier as they slide down the hill. This can also be determined using kinematic equations.

4. Velocity: The velocity of the skier at a specific point during the slide. This can be calculated using kinematic equations.

5. Displacement: The displacement of the skier, which is the change in position from the starting point to the final point. This can be calculated using the distance and the angle of the incline.

Now, let's solve for some of these quantities. Let's start with time:

To find time, we can use the kinematic equation:

distance = (initial velocity * time) + (0.5 * acceleration * time^2)

Since the skier starts at rest (initial velocity = 0), the equation simplifies to:

distance = 0.5 * acceleration * time^2

Plugging in the known values:
30 meters = 0.5 * acceleration * time^2

Now we need to determine the acceleration. The only force acting on the skier parallel to the incline is the component of the weight force:

Force parallel to incline = m * g * sin(theta)

m = 52 kg (given)
g = 9.8 m/s^2 (acceleration due to gravity)
theta = 12 degrees (angle of incline)

Force parallel to incline = 52 kg * 9.8 m/s^2 * sin(12 degrees)

Now we can calculate the acceleration:

acceleration = Force parallel to incline / mass
acceleration = (52 kg * 9.8 m/s^2 * sin(12 degrees)) / 52 kg

Now that we have the acceleration, we can substitute it back into the equation for time:

30 meters = 0.5 * (acceleration) * time^2

Simplify and solve for time.

Once we have time and the acceleration, we can calculate other quantities like velocity and displacement using relevant kinematic equations.

Note: The specific numerical values for these quantities can only be determined by performing the calculations.