Draw free body diagramm of all forces acting on skier

[joemama69]

Homework Statement

A skier of mass m is skiing down a frictionless slope. the skier starts form rest at t = 0 and is subject to a velocity dependent drag force due to air resistance of the form F = -bv, where b is a constant.

a)draw free body diagramm of all forces acting on skier

b) wire a differential equation that can be used to solve for the velocity of the skier as a function of time

c) find expression for Terminal velocity

d) solve b and ditermine the velocity of the skier as a function of time

Homework Equations

The Attempt at a Solution

a) note the attached diagramm. does the the wind come parallel to the hill of horizontally

b)

F_x = ma = mgsin\theta - bv

v = (mgsin\theta - ma)/b

i believe i need to find an equation for a which involvs t, do i just use one of the kinematic equations

the answer is v(t) = (mg sinθ / b) (1 – e^-bt/m) where did the who e part come from

 

[Redbelly98]

The Attempt at a Solution

a) note the attached diagramm. does the the wind come parallel to the hill of horizontally

Since the air resistance force is -bv, it is directly opposite to the direction of the skier's velocity. Is the skier's velocity parallel to the hill or horizontal?
The attachment seems to be missing.

b)

F_x = ma = mgsin\theta - bv

v = (mgsin\theta - ma)/b

i believe i need to find an equation for a which involvs t, do i just use one of the kinematic equations

the answer is v(t) = (mg sinθ / b) (1 – e^-bt/m) where did the who e part come from

It cannot come from the kinematic equations, which only work when acceleration is constant.

It comes from the equation you wrote in part (b),

ma = mg sinθ - bv​

Hint: what equation defines a in terms of v?

 

[joemama69]

Sorry, here's the attachment

the velocity is parallel to the ground.

What do you mean by it came from the equation from part b, i can't plug the inquation into itself

 

[Redbelly98]

Your free body diagram looks good.

the velocity is parallel to the ground.

Correct.

What do you mean by it came from the equation from part b, i can't plug the inquation into itself

True, lol. No, you need to substitute another expression in for a first. Refer to my hint:

Hint: what equation defines a in terms of v?

 

[joemama69]

a = dv/dt