How can there be two answers for this problem?

Question

This is a problem involving an equation relating the time it takes for an object to be dropped and the height from which it is dropped (kinematic). I have the following from MyMathLab on Inverse Functions:

Notice that plugging in the exact value from which 2.85 is derived works as an answer as well, I do not know why I was marked incorrect. Plugging in both values gives 80 meters as the original height.

The 2.85 is rounded off from 2.857142857...

H(t) = 120 - 4.9(2.85714...)^2= 80 meters

H(t) = 120 - 4.9(4.04)^2 = 80 meters

2 questions: 1.How can there be 2 different answers (doesnt make any logical sense)? 2. What did I do wrong? Here I assume that there cannot be 2 answers and I plugged in 80 into the inverse equation and solved, seeing as how the MathLabs answer works and mines does not, something I did must be wrong. Thanks!

Answer 1

Putting in $4.04\dots$ does not give $H=80$ - it gives $H=40$.

Since we started at $H=120$, we are looking for when the object has fallen $80m$, at which point its height would be $40m$. This is why the answer is $4.04$. Your mistake was that you computed the time taken for the object to fall by only $40m$, to a height of $80m$.

Answer 2

There is only one correct answer.

The problem is that you asnwered the wrong question: You answered

How long will it take the rock to fall from 120m to a height of 80m?

But the question was (with clarification)

How long will it take the rock to fall by 80m?

Answer 3

The question asks you to find the time it takes a rock to fall 80m. That is, it asks for the time for the rock to reach a height 80m below its initial height, i.e. 40m. You calculated the time that it takes the rock to fall to a height of 80m.

Also, posting just pictures is frowned upon; you should post a text version.