Accel 1-D HW: Solving for Time with Quadratic

[khzak1]

Homework Statement

A baseball is thrown by Joey from the third floor of his home at 20.0m/s [downwards], his friend Timmy is 3.5 m below him.
a. Find how long it takes the ball to reach Timmy.

I used the quadratic formula to solve to time but I am confused about it in my calculations.

Homework Equations

D=V[1]t+1/2(a)(t)^2
1/2(a)(t)^2 + V[1]t + (-D)

The Attempt at a Solution

Once I find the roots using the quadratic equation, how do I find the time? AHH I'm so confused.

20± √468.67
-9.81

 

[billy_joule]

The Attempt at a Solution

Once I find the roots using the quadratic equation, how do I find the time? AHH I'm so confused.

20± √468.67
-9.81

There are two roots, one is negative, one is positive, does a negative time make any sense as a solution to your problem?
In other words, can Timmy catch the ball before Joey throws it?

 

[khzak1]

So the positive answer relative to time would be
Δt=0.168s approximately

I am not sure if that is the correct answer. Could you confirm it please.

 

[billy_joule]

So the positive answer relative to time would be
Δt=0.168s approximately

I am not sure if that is the correct answer. Could you confirm it please.

It's always to confirm it for yourself, I'm just a stranger on the internet

Plug t = 0.168 s, v = 20 m/s and a = g into your first equation and see if d comes out as 3.5 m (or close to it due to rounding)

 

[khzak1]

Haha, thanks mate ! :)

 

[khzak1]

Something just came to my mind. What if there was a similar question, and I would get a positive integer either way. How would I know which time is correct according to ± ?

 

[billy_joule]

Something just came to my mind. What if there was a similar question, and I would get a positive integer either way. How would I know which time is correct according to ± ?

There should be clues in the problem statement. Imagine a basket ball thrown in a parabola towards the hoop, there will be two positive times where the ball will pass through the same height as the hoop, once on the way up and once on the way down. The second time points are scored (ball passes downward through the hoop) and the first time no points are scored (pall passes upward through the hoop), the question statement will make it clear which time is correct.