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Ahat [919]
3 years ago
9

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 e

ducational 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?
Mathematics
1 answer:
snow_tiger [21]3 years ago
5 0

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.

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