Projectile Height Calculation: Time to Reach 10m with Given Initial Velocity

[Bartosz]

Well its been a while since I've done any physics problems and I am having a problem with a real simple problem. The problem is:

You know that the height (in m) of a projectile is given by the formula

h = - g * t^2 / 2 + vi * t
where t is the time from launch, g is the acceleration due to gravity (9.8 m/sec2) and vi is the initial vertical velocity component (in m/sec).

Calculate the time at which a projectile will reach a certain height.

vi = 20
desired height = 10

So far i have this done, but i always get a negative number and the answers should be 0.58 sec and 3.50 sec.

10 = -9.8t^2/2 + 20t

10(2 + 20t) = -9.8t^2
20 + 200t = -9.8t^2

9.8t^2 + 200t + 20 = 0

(-200 + sqrt(200^2 - 4(9.8*20)) / 2(9.8)
-200 + sqrt(40000 - 784)) / 19.6
(-200 + 198.0303)/19.6

Im sure its just a stupid math mistake, but i can't find it. Also where we even given the correct equation?

 

[iNCREDiBLE]

10 = -9.8t^2/2 + 20t
<={this is the step where your mistake is done}=>
10 - 20t = -9.8t^2/2
<==>
20 - 40t = -9.8t^2
<==>
9.82t^2 - 40t + 20 = 0
and not 9.8t^2 + 200t + 20 = 0

 

[Bartosz]

Thanks a lot, wow don't i feel stupid now