Mechanics- force and motion in one dimension ?
A flare of mass 0.5kg is fired vertically upwards with speed 30m/s. The flare itself provides a force of 0.8N upwards, even when the flare is falling, to keep the flare high as long as possible. The flare is visible over the horizon when it reaches a height of 25m.
a) Find how long the flare is visible for.
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The upward force of the flare "reduces" the gravitational acceleration from 9.8 m/s^2 downward, to 8.2 m/s^2 downward. Because 9.8 - (0.8/0.5) = 8.2. So the motion is described by:
h = (30 m/s)t - (1/2)(8.2 m/s^2)t^2
Now set h = 25m, and you get
4.1 t^2 - 30 t + 25 = 0 =>
t = (30/8.2) +/- (1/8.2)*sqrt(900 - 410).
The period of visibility is (1/4.1)*sqrt(900 - 410) = 5.4 seconds.