How far do acorns drift in the wind?

[nick-metersecondsq]

Homework Statement

we live under a lot of trees, including great oaks. How far can wind carry a falling acorn?

acorn mass: 4.5g
acorn size and shape: r=3cm (assuming sphere)
height of fall: 27m
air density 1.225 kg/m3

Relevant Equations

this is open

this one is our extra credit problem with no instructions. just creative thinking.

 

[Herman Trivilino]

It seems you would need to assume a wind speed and direction.

 

[.Scott]

Acorns rely on ground transportation (mostly squirrels and chipmunks).
When they drop, they generally stay within the trees immediate shade/shed zone.

 

[nick-metersecondsq]

sorry I left that off. speed is 25 m/s and direction is parallel to the ground.

 

[phinds]

So what attempt have you made to solve the problem yourself? We don't spoon feed answer, but rather help people who are trying to help themselves.

 

[berkeman]

Thread closed for Moderation...

 

[berkeman]

Thread is reopened provisionally.

@nick-metersecondsq -- Please show your best efforts to work on this problem so that the thread can remain open. It is important for you to list the Relevant Equations involved.

 

[Herman Trivilino]

sorry I left that off. speed is 25 m/s and direction is parallel to the ground.

Please post a complete statement of the given problem. There are relevant equations, so please post what you think they might be and tell us why. We need to understand the problem as well as your attempt at solving it.

 

[nick-metersecondsq]

It seems you would need to assume a wind speed and direction.

Thread is reopened provisionally.

@nick-metersecondsq -- Please show your best efforts to work on this problem so that the thread can remain open. It is important for you to list the Relevant Equations involved.

so far I know t = √(2h/g gives me time ... so t=sqrt(2(27)/9.8 = 2.35s

Force of wind is F = 0.5 * p * v^2 * A * Cd. i'm assuming drag coeff of 1.2?

F=2.6
mass of wind = density * area = M= 1.229 kg/m3 * (3 pi r2 = .000084*1.229= .00010

I need F=ma, solving for A since I have t and need distance.
but maybe my algebra is wrong, but that gives me A=F/m = 206000 ms2 (which is bonkers).
and that's where I'm lost.

 

[jbriggs444]

so far I know t = √(2h/g gives me time ... so t=sqrt(2(27)/9.8 = 2.35s

That is with the assumption of zero air resistance.

Force of wind is F = 0.5 * p * v^2 * A * Cd. i'm assuming drag coeff of 1.2?

That is with the assumption of non-zero air resistance.

Maybe you could try computing terminal velocity and compare that with the landing velocity under the assumption of free fall.

Or maybe you could compare terminal velocity with wind velocity.