SOLUTION: A signal flare is fired upward from ground level at an initial speed of 294 m/s. A balloon is at 2450m and passes it. How long will it be before the flare passes the balloon going

Question 295516: A signal flare is fired upward from ground level at an initial speed of 294 m/s. A balloon is at 2450m and passes it. How long will it be before the flare passes the balloon going down?
(The answer is 40 sec but I don't understand how to get that)
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
The flare is acting under the force of gravity with an initial upward velocity.

where g is the gravitational constant (9.8 m/s^2), y is the flare's position from the ground (y=0 on the ground and moves positively upwards), t is time. C1 and C2 are constants that you solve for using your initial conditions.
is velocity, the first derivative of position.
is acceleration, the second derivative of position, first derivative of velocity.
You know the initial velocity (t=0).

.
.
.
You also know the initial position (t=0). The flare is on the ground (y=0).

Now you have the complete equation for the flare's position as a function of time.

Solve for t when the flare is at the balloon position,.

Use the quadratic formula,

At time seconds, the flare passes the balloon going up and at seconds the flare passes the balloon going down. So seconds after the flare passes the balloon going up, it will pass the balloon going down.
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