# Antigravity in the summertime

Summer is coming (for some of us) and you're trying out your new water guns. Your test involves hovering a cafeteria tray in midair by shooting it with a stream of water from your gun. Whichever gun can suspend the tray at the greatest height is the winner.

Suppose your best gun shoots water upward with an initial velocity $$v_0$$, and that the weight of your tray is $$M$$, what is the height $$h_\text{max}$$ (in meters) at which the tray hovers at rest?

Assumptions and Details

• $$v_0=20$$ m/s
• $$M=1.5$$ kg
• The flux of water from the tip of the gun is $$J_m = 0.45$$ kg/s
• Take $$g = 9.8$$ m/s$$^2$$
• Assume that the water comes straight down after hitting the tray, i.e. the collision is elastic (practically, this can be achieved if the spray has a slight radial spread as it travels upward).
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