# Free fall problem involving two objects

## Homework Statement

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

Vf = Vi+gt
d=Vit-0.5gt2

## 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

ehild
Homework Helper
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

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

I see. Thank you very much :)