# Free fall problem involving two objects

1. Jul 26, 2010

### Dragonite

1. The problem statement, all variables and given/known data
A stone is thrown vertically into the air from a tower 110 ft. high at the same time that a second stone is thrown upward from the ground. The initial velocity of the first stone is 60 ft/s and that of the second stone 85 ft/s. When and where will the stones be at the same height from the ground?

*note* When I asked my teacher, he said the "thrown vertically" meant that the stone was thrown upward

2. Relevant equations
Vf = Vi+gt
d=Vit-0.5gt2

3. The attempt at a solution

I have two solutions. One by me and the other from my classmate. According to the teacher, her solution is correct, but I disagree.

*Solution of classmate*

Conversion of units:

110ft = 33.53m
60ft/s = 18.29m/s
85ft/s = 25.91m/s

d1+33.53m=d2
18.29t - 4.9t2 + 33.53 = 25.91t - 4.9t2
33.53 = 25/91t - 18.29t
t = 4.4s
18.29 (4.4) - 4.9 (4.4)2 + 33.53 = 19.13m

*My solution* - I believe that my classmate failed to take into account the first stone being thrown upwards. However, there is also something wrong with my solution.

Conversion of units:

110ft = 33.53m
60ft/s = 18.29m/s
85ft/s = 25.91m/s

18.29 = 9.8t
1.87 = t
18.29(1.87) - 0.5(9.8)(1.87)2 + 33.53 = d of stone 1 at 1.87s from the ground
d = 50.6m

25.91 = 9.8t
2.64 = t
25.91(2.64) - 0.5(9.8)(2.64)2 = d of stone 2 at 2.64s from the ground
d = 34.25

2.64 - 1.87 = 0.77s
9.8(0.77) = V
d = 2.91m
50.6 - 2.91 = 47.69m = d of stone 1 at 2.64s from the ground

47.69 - (7.55t + 0.5(9.8)t2) = 34.25 - (0.5(9.8)t2
13.44 = 7.55t
t = 1.78s
Plugging in t to the formula for t, d = 28.96m
47.69 - 28.96 = 18.73 m
1.78 + 2.64 = 4.42s

Therefore, my answer is 4.42 s at 18.73 m from the ground

2. Jul 26, 2010

### ehild

The solution of your classmate is correct. Your piecewise solution might be correct, but unnecessarily complicated with a lot of rounding errors. That can be the reason of the different results.

ehild

3. Jul 27, 2010

### Dragonite

I see. Thank you very much :)