The function of the water balloon is an illustration of a quadratic function.
The balloon will splat on the ground after 2.5 seconds
The function is given as:
[tex]h(t) = -6t^2 + 13t + 5[/tex]
When the balloon splats on the ground, the value of h(t) is 0.
So, we have:
[tex]-6t^2 + 13t + 5 = 0[/tex]
Expand the expression
[tex]-6t^2 + 15t- 2t + 5 = 0[/tex]
Factorize the above expression
[tex]-3t(2t - 5)- 1(2t - 5 )= 0[/tex]
Factor out 2t - 5 in the 2t - 5
[tex](-3t - 1)(2t - 5 )= 0[/tex]
Split the equation into 2
[tex]-3t - 1 = 0\ or\ 2t - 5= 0[/tex]
Rewrite as:
[tex]-3t = 1\ or\ 2t = 5[/tex]
Solve for t
[tex]t = -\frac 13\ or\ t = \frac 52[/tex]
The value of t cannot be less than 0 i.e. negative.
So, we have
[tex]t = \frac 52[/tex]
Divide 5 by 2
[tex]t = 2.5[/tex]
Hence, the balloon will splat on the ground after 2.5 seconds
Read more about quadratic functions at:
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