Solve for Impact Speed of 0.25kg Pine Cone Falling 20m

[get_rekd]

A 0.25 kg pine cone falls from a branch 20 meters above the ground.

a) What speed would it hit the ground if the air resistance could be ignored?

I am not too sure how to do this but this is what I've got so far:

m=0.25
g=9.8 m/s^2
F=2.45 J
h=20 m

Ep=(0.25kg)(9.8m/s)(20m) Ek=1/2mv^2
=4.9J 4.9J=1/2(0.25kg)(v^2)
2(4.9J=1/2(0.25kg)(v^2))
9.8J=(0.25kg)(2v^2)
-0.25 -0.25
9.55J=2v^2
------------
2
4.775 = v^2
root 4.775 = 2.2 m/s = v ?

is this even close to correct. I think I am doing something wrong

 

[Midy1420]

right method...check your calculations

 

[get_rekd]

I am also not sure in my calculation of Potential Energy wether
Ep=(0.25kg)(9.8m/s^2)(20m)
= 4.9 or 49

 

[get_rekd]

A 0.25 kg pine cone falls from a branch 20 meters above the ground.

a) What speed would it hit the ground if the air resistance could be ignored?

I am not too sure how to do this but this is what I've got so far:

m=0.25
g=9.8 m/s^2
F=2.45 J
h=20 m

Ep=(0.25kg)(9.8m/s)(20m) Ek=1/2mv^2
=4.9J 4.9J=1/2(0.25kg)(v^2)
2(4.9J=1/2(0.25kg)(v^2))
9.8J=(0.25kg)(2v^2)
-0.25 -0.25
9.55J=2v^2
------------
2
4.775 = v^2
root 4.775 = 2.2 m/s = v ?

is this even close to correct. I think I am doing something wrong

Ep=(0.25kg)(9.8m/s)(20m) Ek=1/2mv^2
=49J 49J=1/2(0.25kg)(v^2)
2(4.9J=1/2(0.25kg)(v^2))
98J=(0.25kg)(2v^2)
-0.25 -0.25
97.75J=2v^2
------------
2
48.87 = v^2
root 48.87 = 6.9 m/s = v ?
Would this be correct then?

 

[Midy1420]

looks good...answer makes more sense

 

[get_rekd]

Thanks a lot!

 

[get_rekd]

So there is a part B to the problem:

If it actually hits the ground with a speed of 9.0 m/s, what was the average force of air resistance on it?

Since I got a velocity of 6.9 m/s with 0 air resistance in the first part of the problem wouldn't there be some force accelerating this cone in this part? Because a falling cone with air resistance should hit the ground slower than a cone with no air resistance?

 

[Midy1420]

watch your algebra in part (a)

 

[get_rekd]

Is it still wrong? I cannot seem to find where I made a mistake? Which section of the calculation?