A signal flare is fired upward from ground level with an initial speed of 294 m/s. A balloonist cruising at a height of 2450 m sees it pass on the way up. How long will it be before the flare passes the balloonist again on the way down?

A signal flare is fired upward from ground level with an initial speed of 294 m/s. A balloonist cruising at a height of 2450 m sees it pass on the way up. How long will it be before the flare passes the balloonist again on the way down?

Since we're using metric, try the quadratic h(t)=-4.9t^{2}+294t to model the path of the flare. Set this equal to 2450 and solve for t. There will be two solutions. One for on the way up and one for on the way down. What is the difference between those times? That is how long it'll be until the balloonist sees the flare again.

Use the formula s = ut + \frac12 at^2.

You'll have a quadratic in t. s is the height of the balloonist, u the initial velocity, and a the acceleration due to gravity.

Solve for t. You'll have two values for t. The difference between the two give the time interval.

EDIT: Oops, I typed, had to go away, ans pressed 'post' and saw your post galactus... sorry :o