An object is launched at 19.6 m/s from a 58.8 m tall platform. The equation for the object's height above the ground (y) at time tseconds is
y = –4.9t2 + 19.6t + 58.8
Use the quadratic formula to find the roots of this equation.
What do these numbers represent?
I assume you know that quadratic formula.
The roots are where the height is zero -- that is, when the object leaves or returns to the ground.
Yes yes, I have found the roots. I'm not sure I understand the second question. Is the question asking about the roots?
so, what is confusing about my second sentence?
No not your question my original question. I meant What do these numbers represent? I don't understand what numbers
THE ROOTS are where y=0
That is, when the object hits the ground!
since one root is negative, it does not count. That is how long ago you'd have had to launch the object to get it to an altitude of 58.8 when you started measuring (t=0)
To find the roots of the quadratic equation y = -4.9t^2 + 19.6t + 58.8, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a, b, and c represent the coefficients of the variables in the quadratic equation:
a = -4.9
b = 19.6
c = 58.8
Substituting these values into the quadratic formula, we get:
t = (-19.6 ± √(19.6^2 - 4(-4.9)(58.8))) / (2(-4.9))
Simplifying further:
t = (-19.6 ± √(384.16 + 1138.32)) / (-9.8)
t = (-19.6 ± √1522.48) / (-9.8)
Now, we can find the square root of 1522.48:
√1522.48 = 39.03
So, t = (-19.6 ± 39.03) / (-9.8)
Now we have two possible values for t:
t1 = (-19.6 + 39.03) / (-9.8)
t2 = (-19.6 - 39.03) / (-9.8)
Simplifying further:
t1 = 19.43 / (-9.8)
t2 = -58.63 / (-9.8)
Now we can calculate the values of t1 and t2:
t1 ≈ -1.98
t2 ≈ 5.98
Therefore, the roots of the quadratic equation y = -4.9t^2 + 19.6t + 58.8 are t ≈ -1.98 and t ≈ 5.98.
These numbers represent the values of time (t) at which the object will reach the same height as the ground (y = 0). In other words, these are the times at which the object will hit the ground or land.