Falling from a Tree: Anastasia & Joe's Adventure

[StotleD]

While exploring the canopy of the rainforest in equatorial South America, Anastasia falls from a branch 31.0 meters high. Exactly 1.4 seconds later Joe falls from the same branch. How high above the ground is Joe when Anastasia splats into the mud below? undefined

 

[mathmike]

this sounds almost to easy.

y = y0 -1/2 * g* t ^2

y = 31 - 1/2 * 9.8 * (1.4) ^ 2

do the math

 

[StotleD]

I get 21.40m (21.396 m) but the computer I am doing it on cross checks my answer and says its wrong...

 

[HallsofIvy]

this sounds almost to easy.

y = y0 -1/2 * g* t ^2

y = 31 - 1/2 * 9.8 * (1.4) ^ 2

do the math

Yes, it was too easy. That is Anastasia's height when Joe starts to fall. To find Joe's height when Anastasia hits the ground:

1) Solve 31- (1/2)(9.8)t² to find time t when Anastasia hits the ground.

2) Put that value of t into h= 31- (1/2)*(9.8)(t- 1.4)² to find Joe's height h.

 

[mathmike]

i didnt want to do the whole problem for them, but yes halls is right

 

[mukundpa]

For what time Joe is in motion when Anastasia splats in mud? is it 1.4 sec ?

 

[HallsofIvy]

No, as I said before, solve (1/2)(9.8)t²- 31= 0 (her height will be 0) to find when Anastasia hits the ground.

 

[StotleD]

This is Anastasia's height. I'm trying to find Joe's...

 

[geosonel]

This is Anastasia's height. I'm trying to find Joe's...

joe's height will be
h_joe = 31 - (1/2)*(9.8)(T_A - 1.4)^2
where T_A is when A hits the mud found by solving
(1/2)(9.8)(T_A)^2 = 31

 

[DAS]

StotleD: First I calculated how long it takes Anastasia to fall before hitting the ground. I came up with 2.52 seconds. If Joe falls 1.4 s after Anastasia does, and if she hits the ground after 2.52 s, then he has fallen for 1.12 s when she hits. You can calculate his distance fallen of distance above the ground or both. I got 6.15 m that Joe fell. 31.0 m - 6.15 m is the height above the ground: 24.85 m. Does that help and match your understanding and calculations?
DAS