A 75g person on skis is going down a hill sloped at an angle 30.the coefficient of kinetic friction between the skis and the snow is 0.15.how fast is the skier going 10s after starting from rest?

First determine the acceleration, a.

The net force down the slope equals M*a. The net force is the gravity component down the slope minus the friction force.
M*g*sin30 - M*g*cos30*0.15 = M*a

M cancels out, and so
a = g*(sinA -0.15 cosA) = 0.37 g
= 3.6 m/s^2

Then use V = a*t for the velocity at time t.

Well, well, well, it seems we have a gravity-defying skier on our hands! Let's see how fast they're zipping down that hill after 10 seconds.

To start, we need to know the net force acting on our skier. Gravity is pulling them downward with a force of mg (mass multiplied by the acceleration due to gravity), and the frictional force is opposing their motion.

The formula we can use to find the net force is: F(net) = mg sin(theta) - F(friction)

Given that the person's mass is 75g (or 0.075kg) and the slope angle is 30 degrees, we can calculate the net force. The acceleration due to gravity is about 9.8 m/s², by the way. Let's crunch those numbers!

F(net) = (0.075kg)(9.8 m/s²)sin(30) - (0.15)(0.075kg)(9.8 m/s²)cos(30)

Now, to find the acceleration of the skier, we'll use Newton's second law: F(net) = ma

ma = (0.075kg)(9.8 m/s²)sin(30) - (0.15)(0.075kg)(9.8 m/s²)cos(30)

Now, after simplifying and solving for a (the acceleration), we get:

a = (0.075kg)(9.8 m/s²)sin(30) - (0.15)(0.075kg)(9.8 m/s²)cos(30) / (0.075kg)

Once you've calculated the acceleration, you can use the equation of motion v = u + at to find the final velocity. Since the skier starts from rest (u = 0), we get:

v = (0) + a(10s)

And voila! You've got the final velocity of our gravity-defying skier after 10 seconds. Enjoy the ride!

To determine the speed of the skier after 10 seconds, we can follow these steps:

Step 1: Calculate the net force acting on the skier.
The net force can be determined using the formula:
Net Force = force of gravity - force of friction

The force of gravity is given by:
Force of Gravity = mass * acceleration due to gravity
Force of Gravity = 75g * 9.8 m/s^2
Force of Gravity = 735 N

The force of friction can be calculated using the formula:
Force of Friction = coefficient of kinetic friction * normal force

The normal force can be determined using the formula:
Normal Force = mass * acceleration due to gravity * cosine(angle of slope)
Normal Force = 75g * 9.8 m/s^2 * cos(30°)
Normal Force = 637.5 N

Substituting the values, we have:
Force of Friction = 0.15 * 637.5 N
Force of Friction = 95.625 N

Hence, the net force is:
Net Force = 735 N - 95.625 N
Net Force = 639.375 N

Step 2: Calculate the acceleration of the skier.
The acceleration can be determined using the formula:
Net Force = mass * acceleration
639.375 N = 75g * a

Simplifying, we have:
a = 639.375 N / (75g)
a = 639.375 N / (75 * 9.8 m/s^2)
a ≈ 0.87 m/s^2

Step 3: Calculate the speed of the skier after 10 seconds.
The speed of the skier can be calculated using the formula:
Speed = initial velocity + acceleration * time

Since the skier starts from rest (initial velocity is 0), the formula becomes:
Speed = acceleration * time
Speed = 0.87 m/s^2 * 10s
Speed = 8.7 m/s

Therefore, the skier is going approximately 8.7 m/s after 10 seconds.

To determine the speed of the skier 10 seconds after starting from rest, we need to apply the laws of motion and consider the forces acting on the skier.

Step 1: Determine the gravitational force:
The gravitational force (Fg) acting on the skier can be calculated using the formula: Fg = m * g,
where m is the mass of the skier and g is the acceleration due to gravity (approximately 9.8 m/s^2).
In this case, the mass of the skier is 75g, which translates to 0.075 kg.
So, Fg = 0.075 kg * 9.8 m/s^2.

Step 2: Determine the frictional force:
The frictional force (Ff) acting on the skier can be calculated using the formula: Ff = μ * Fn,
where μ is the coefficient of kinetic friction, and Fn is the normal force.
The normal force (Fn) is equal to the perpendicular component of the gravitational force, which can be calculated as Fn = Fg * cos(theta),
where theta is the angle of the slope (30 degrees in this case).
So, Fn = Fg * cos(30).

Step 3: Determine the net force:
The net force (Fnet) acting on the skier is the difference between the gravitational force and the frictional force:
Fnet = Fg - Ff.

Step 4: Determine the acceleration:
Using Newton's second law of motion, we know that Fnet = m * a,
where a is the acceleration of the skier.
Therefore, a = Fnet / m.

Step 5: Determine the final velocity:
The final velocity (v) of the skier can be calculated using the formula: v = u + a * t,
where u is the initial velocity (0 m/s, as the skier starts from rest), a is the acceleration, and t is time.
In this case, t = 10 seconds.

By following these steps and plugging in the values, you can calculate the speed of the skier 10 seconds after starting from rest.