Differential Equation Question

[Ravi Ramdoolar]

Homework Statement

Felix, a Red bull skydiver, (mass m) who drops out of a hovering helicopter, falls long enough without a parachute(so the drag force has strenght kv² ) to reach his first terminal velocity ( denoted v1). When his parachute opens, the air resistance force has a strenght Kv.

At what minimum altitude must his parachute open so that he slows to within 1% of his new
(much lower) terminal velocity (v2) by the time he hits the ground?

Homework Equations

Newtons second law F = ma

The Attempt at a Solution

I used Newton second law of motion and think i have to use the time t = 0 and not sure what to do again could someone help me

 

[Mark44]

Homework Statement

Felix, a Red bull skydiver, (mass m) who drops out of a hovering helicopter, falls long enough without a parachute(so the drag force has strenght kv² ) to reach his first terminal velocity ( denoted v1). When his parachute opens, the air resistance force has a strenght Kv.

At what minimum altitude must his parachute open so that he slows to within 1% of his new
(much lower) terminal velocity (v2) by the time he hits the ground?

Homework Equations

Newtons second law F = ma

The Attempt at a Solution

I used Newton second law of motion and think i have to use the time t = 0 and not sure what to do again could someone help me

Please show us what you did and we can go from there.

 

[Ravi Ramdoolar]

Please show us what you did and we can go from there.

F=ma
kv=md²x/dt²

kdx/dt=md²x/dt²

from here i don't know where to go i don't even know if this is correct does anyone know how to work it out ?

 

[Ravi Ramdoolar]

F=ma
kv=md²x/dt²

kdx/dt=md²x/dt²

from here i don't know where to go i don't even know if this is correct does anyone know how to work it out ?

This is what i did

 

[tiny-tim]

kdx/dt=md²x/dt²

what about gravity?

 

[Ravi Ramdoolar]

what about gravity?

i don't know i think the gravity will be the acceleration

 

[tiny-tim]

gravity (times mass) is one of the forces on the skydiver

kv is the other force

now use F_total = ma ​

 

[Ravi Ramdoolar]

gravity (times mass) is one of the forces on the skydiver

kv is the other force

now use F_total = ma ​

ok will try something

 

[haruspex]

without a parachute(so the drag force has strenght kv² ) ... When his parachute opens, the air resistance force has a strenght Kv.

Just checking: it's kv² without parachute but Kv with? Not Kv²?

 

[Ravi Ramdoolar]

Just checking: it's kv² without parachute but Kv with? Not Kv²?

yes when the parachute opens it is Kv and before it is Kv² i am mostly sure we have o use the Kv since the question asked when the parachute was open

 

[haruspex]

yes when the parachute opens it is Kv and before it is Kv²

That's not quite what it says in the OP. There you wrote kv², not Kv². I can cope with the change from v² to v as the parachute opens, but it seems very unlikely the coefficient would be the same. For a start, its dimensions would be different.
However, since you're given the first terminal velocity as v1, it's irrelevant what the drag was before the parachute opened. So ignore my questions and concentrate on getting the equation when drag = Kv.

 

[Ravi Ramdoolar]

That's not quite what it says in the OP. There you wrote kv², not Kv². I can cope with the change from v² to v as the parachute opens, but it seems very unlikely the coefficient would be the same. For a start, its dimensions would be different.
However, since you're given the first terminal velocity as v1, it's irrelevant what the drag was before the parachute opened. So ignore my questions and concentrate on getting the equation when drag = Kv.

this is what i did so far

ma = mg - kv (since kv is the opposite direction as the gravitational force)

md²x/dt² = mg - k dx/dt

 

[Ravi Ramdoolar]

this is what i did so far

ma = mg - kv (since kv is the opposite direction as the gravitational force)

md²x/dt² = mg - k dx/dt

this was given

Mass of Felix = 70 kg
Gravity = 9.8ms^-2
Air resistance proportional constant K = 110 kgs^-1
terminal velocity without parachute, v1 = 52ms^-1
Terminal velocity with parachute v2 = 6.2ms^-1

what do i do from here ??

 

[tiny-tim]

ma = mg - kv (since kv is the opposite direction as the gravitational force)

ok, now rewrite that as mdv/dt = mg - kv, and integrate …

what do you get? ​