Answer:
The potato is 224 feet in the air after 2.75 second on the way up and after 5 seconds on the way back down.
Step-by-step explanation:
Given : A potato launched by a particular potato gun has a height described by [tex]h ( t ) =-16 t^2+124 t+4[/tex].
To find : When is the potato 224 feet in the air?
Solution :
When the potato is 224 feet in the air i.e. [tex]h(t)=224[/tex]
Substitute in the equation [tex]h ( t ) =-16 t^2+124 t+4[/tex],
[tex]224=-16 t^2+124 t+4[/tex]
[tex]16t^2-124 t+220=0[/tex]
[tex]4t^2-31t+55=0[/tex]
Applying quadratic formula, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, a=4, b=-31 and c=55
[tex]t=\frac{-(-31)\pm\sqrt{(-31)^2-4(4)(55)}}{2(4)}[/tex]
[tex]t=\frac{31\pm\sqrt{81}}{8}[/tex]
[tex]t=\frac{31\pm9}{8}[/tex]
[tex]t=\frac{31+9}{8},\frac{31-9}{8}[/tex]
[tex]t=5,2.75[/tex]
The potato is 224 feet in the air after 2.75 second on the way up and after 5 seconds on the way back down.
