Free Fall quadratic equation problem

[aron silvester]

The answer based on the answer key is 3 seconds. I used the quadratic equation to solve for t. My question is how do we know what sign to use when solving for the final value? For this problem, I had to use the negative sign, but I knew that I needed to use the negative sign because I already know the final answer. Using the plus sign would give me 3.4 seconds.

 

[NFuller]

Using the plus sign would give me 3.4 seconds

Using the plus sign gives you -3.4 seconds. Since you are looking for a positive value of time, you need to use the sign which gives a positive answer.

The reason the negative time solution exists is because if you extend the shape of the parabola in your drawing to the left past the origin, the parabola will intercept the t-axis again at a negative time. The quadratic formula gives you both points where the parabola intersects the t-axis and you need to select which answer to use based on physical constraints. In this case, the constraint is that time is positive.

 

[berkeman]

The answer based on the answer key is 3 seconds. I used the quadratic equation to solve for t. My question is how do we know what sign to use when solving for the final value? For this problem, I had to use the negative sign, but I knew that I needed to use the negative sign because I already know the final answer. Using the plus sign would give me 3.4 seconds.

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