Quadratic Equation Help?

Question

I got this question from a website:

An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. The equation for the object's height s at time t seconds after launch is s(t) = –4.9t2 + 19.6t + 58.8, where s is in meters. When does the object strike the ground?
What is the height (above ground level) when the object smacks into the ground? Well, zero, obviously. So I'm looking for the time when the height is s = 0. I'll set s equal to zero, and solve:

0 = –4.9t2 + 19.6t + 58.8
0 = t2 – 4t – 12
0 = (t – 6)(t + 2)

Then t = 6 or t = –2. The second solution is from two seconds before launch, which doesn't make sense in this context. (It makes sense on the graph, because the line crosses the x-axis at –2, but negative time won't work in this word problem.) So "t = –2" is an extraneous solution, and I'll ignore it.



So what would happen if both answers were positive. What would be the answer?

Answer 1

The equation for a body falling a negative distance AWAY from a center of gravity (or, rather TOWARD that same center) is written as:

s = ut - (1/2 * (at^2)) + s'

Since the squared term is negative in this equation, it WILL ALWAYS BE the product of a positive number and a negative number.

In this case, you can't get two positive results.

Answer 2

In this kind of questions 2 positive answers are impossible. the same object, under the same conditions can't hit the ground in two different times. So you will always get only one positive answer.

Unless the condition or the object changes, the time will always be the same.

Answer 3

if the object bounced, it would hit the ground twice and give two positive answers.
usually an answer with 2 positive roots indicates when the object passea a certain height while going up and then passes that same height on the way down.

Answer 4

Then the object must have struck the ground twice. This could happen only you you take in account the object bouncing or else you will always get one non positive root along with your answer.

Answer 5

In theory, two positive numbers should never be an option. This is because "a" will always be a negative number. ("a" being -4.9 in this problem). Since this number is negative you will have to multiply to opposite signed numbers to achieve the correct answer. This, then, will give you both a positive and negative answer and you should choose the positive one, as you know.

Answer 6

As you quite rightly said, only one solution makes sense, hence you would use this solution.

Unless you have the ability of time travel (or the object has) it is impossible to land 2 seconds before you were thrown.

You will find with problems such as this, that only one answer will ever be positive (your teacher or textbook will always do it like that.)