Question

A potato gun is a device made out of plastic pipe that launches a potato using compressed air. They can be great fun, and even educational for physics and math, as this question illustrates. A potato launched by a particular potato gun has a height described by h ( t ) = − 16 t 2 + 124 t + 4 h(t)=-16t2+124t+4. When is the potato 224 feet in the air?

Answer 1

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  $h ( t ) =-16 t^2+124 t+4$.

To find : When is the potato 224 feet in the air?

Solution :

When the potato is 224 feet in the air i.e. $h(t)=224$

Substitute in the equation $h ( t ) =-16 t^2+124 t+4$,

$224=-16 t^2+124 t+4$

$16t^2-124 t+220=0$

$4t^2-31t+55=0$

Applying quadratic formula, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, a=4, b=-31 and c=55

$t=\frac{-(-31)\pm\sqrt{(-31)^2-4(4)(55)}}{2(4)}$

$t=\frac{31\pm\sqrt{81}}{8}$

$t=\frac{31\pm9}{8}$

$t=\frac{31+9}{8},\frac{31-9}{8}$

$t=5,2.75$

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.