problem solver equation

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 . When is the potato 147 feet in the air?The potato is 147 feet in the air after_______________  seconds ?on the way up and after _______________ seconds on the way back down.?

Answer 1

There are two approaches to this problem: the quadratic formula and the graphical method

(1) Quadratic formula:

The general form to the equation above is: ax+bx+c =0, so we can modify the equation above to look like

-16 t² + 100 t -144 = 0.

Then we can just use the quadratic formula, which looks like:

x = (1/(2a))(-b ± (b²- 4ac)^1/2)

which for this problem looks like:

t = (1/(2*-16))(-100 ± (100²- 4(-16)(-144))^1/2)

t = 2.25, 4

(2) The graphical way would be to plot -16 t² + 100 t -144 = 0 and see that the roots are at: t = 2.25 and t = 4.

so the answer is that the potato is at 147 feet on the way up at 2.25 seconds and at the same height on the way down at 4 seconds.