(adsbygoogle = window.adsbygoogle || []).push({}); 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

V_{f}= V_{i}+gt

d=V_{i}t-0.5gt^{2}

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

d_{1}+33.53m=d_{2}

18.29t - 4.9t^{2}+ 33.53 = 25.91t - 4.9t^{2}

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)t^{2}) = 34.25 - (0.5(9.8)t^{2}

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

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# Free fall problem involving two objects

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