A cross-country skier slides horizontally along the snow and comes to rest after sliding a distance of 11 m. If the coefficient of kinetic friction between her skis and the snow is μk = 0.020, determine her speed at the start of the slide.

2.10m/s

Here, we use the work-energy principle that states that the work done (W) on a body is equal to the change in kinetic energy (Δ) of the body. i.e

W = Δ        [Δ = ₂ - ₁]

=> W = ₂ - ₁           ----------------(i)

[₂ = final kinetic energy ₁ = initial kinetic energy]

But;

W = F x s cos θ

Where;

F = net force acting on the body

s = displacement of the body due to the force

θ = angle between the force and the displacement.

Also;

₂ = x m x v²

₁ = x m x u²

Where;

m = mass of the body

v = final velocity of the body

u = initial velocity of the body

Substitute the values of ₂ , ₁ and W into equation (i) as follows;

F x s cos θ =  ( x m x v²) - ( x m x u²)    -----------------(ii)

From the question;

i. The skier comes to a rest, this implies that the final velocity (v) of the body(skier) is 0.

Therefore substitute v = 0 into equation (ii) to get;

F x s cos θ =  ( x m x 0²) - ( x m x u²)

F x s cos θ =  0 - ( x m x u²)

F x s cos θ =   - ( x m x u²)             ---------------------(iii)

ii. Since there is no motion in the vertical direction, the net force (F) acting is the kinetic frictional force () in the horizontal direction

i.e F =

But we know that the frictional force , is given by;

F = = μk x N

Where;

μk = coefficient of static friction

N = Normal reaction which is equal to the weight (m x g) of the skier [since there is no motion in the vertical]

=> F =    = μk x m x g          [m = mass of the skier and g = acceleration due to gravity]

iii. Also, since the only force acting is the frictional force acting to oppose motion, the angle θ between the force and the displacement is 180°

iv. Now substitute all of these values into equation (iii) as follows;

F x s cos θ =   - ( x m x u²)

μk x m x g x s cos θ = -  ( x m x u²)

Divide through by m;

μk x g x s cos θ = -  ( x u²)        ----------------(iv)

From the question;

s = 11m

μk = 0.020

Take g = 10m/s²

θ = 180°

Substitute these values into equation (iv) and solve for u;

0.020 x 10 x 11 cos 180 = -  ( x u²)

0.020 x 10 x 11 x (-1) = -  ( x u²)

-2.2 = -   x u²

u² = 4.4

u =

u = 2.10m/s

Therefore, the speed of the skier at the start of the slide is 2.10m/s

explanation:

earth's surface is mainly heated by the absorption of infrared radiation from the sun.

evaporation occurs because molecules in liquid water are warmed ( usually by the sun) and vibrate quicker, becoming less dense and rise.

condensation occurs because molecules in water vapor are cooled and therefore vibrate more slowly thus becoming more dense and eventually fall to earth.

lines of equal barometric pressure on a weather map are called: isobars : lines of equal temp on a weather map are called: isotherms.​

answer: (431,2)

step-by-step explanation: