Height:
[tex]h=-16t^2+73t+18[/tex]
As we are asked the time when h = 91ft, then we have to set the equation to 91:
[tex]91=-16t^2+73t+18[/tex]
Now, we can solve for t by using the General Quadratic Equation:
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
in which the variables represent the coefficients of a quadratic equation in the form:
[tex]ax^2+bx+c=0[/tex]
Therefore, we have to set our equation to 0:
[tex]0=-16t^2+73t+18-91[/tex]
Simplifying:
[tex]0=-16t^2+73t-73[/tex]
Thus, in our case:
• a = -16
,
• b = 73
,
• c = 73
Replacing these values in the formula:
[tex]t_{1,2}=\frac{-73\pm\sqrt[]{73^2-4\cdot(-16)\cdot(-73)}}{2\cdot(-16)}[/tex]
Simplifying:
[tex]t_{1,2}=\frac{-73\pm\sqrt[]{657}}{-32}[/tex][tex]t_1=\frac{-73+3\sqrt[]{73}}{-32}\approx3.08s[/tex][tex]t_2=\frac{-73-3\sqrt[]{73}}{-32}\approx1.48s[/tex]
As the object is thrown at 73ft/s, at 3 seconds it would be more or less three times higher than 73ft.
Answer: 1.48s
