The approximate time it takes for the rock and the bird to be at the same height is 1.68 seconds.
The height of the seagull above the sea is given by:
[tex]h=3t[/tex]
The height of a rock falling off a cliff above the sea is given by:
[tex]h=-16t^{2} +50[/tex]
What is a solution to the system of two equations?
A solution to the system of two equations is the value of the independent variable that satisfies both equations.
So, the approximate time it takes for the rock and the bird to be at the same height will be given by:
[tex]3t=-16t^{2} +50[/tex]
[tex]16t^{2} +3t-50=0[/tex]
[tex]t=\frac{-3+\sqrt{9-4*16*(-50)} }{2*16}[/tex]
[tex]t=1.68[/tex] seconds.
Thus, the approximate time it takes for the rock and the bird to be at the same height is 1.68 seconds.
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