A flare fired from the bottom of a gorge is visible only when the flare is above the rim. if it is fired with an initial velocity of 96 ft/sec....

[alyren]

A flare fired from the bottom of a gorge is visible only when the flare is above the rim. if it is fired with an initial velocity of 96 feet per second, and the gorge is 128 feet deep, during what interval can the flare seen? ( h=16t^2+v0t+h0).

is this equation setup right? h = 16t^2 + 96t + 128
is so do factor afterward?

 

[BigGlenntheHeavy]

\(\displaystyle s(t) \ = \ h(t) \ = \ -16t^2+96t-128\)

 

[alyren]

may i ask why does the sign change to negative?

 

[Mrspi]

may i ask why does the sign change to negative?

Sure you may ask! And here's my two cents worth.

In the first place, the coefficient of t[sup:2dwtov4s]2[/sup:2dwtov4s] represents the acceleration of gravity...which is in the downward direction (hence, negative).

In the second place, the origination of the rocket is at the bottom of a canyon...BELOW the surface of the earth. So, its elevation with respect to the surface is NEGATIVE....thus the -128 in the formula.

 

[BigGlenntheHeavy]

\(\displaystyle OK, \ now, \ assuming \ the \ only \ force \ acting \ on \ the \ flare \ is \ that \ due \ to \ gravity,\)

\(\displaystyle and \ neglecting \ air \ resistance, \ the \ height \ is \ given \ by \ the \ position \ function:\)

\(\displaystyle s(t) \ = \ h(t) \ = \ \frac{1}{2}gt^2+v_ot+s_o \ where \ g \ = \ -32ft./sec^2, \ is \ the \ acceleration\)

\(\displaystyle due \ to \ gravity, \ v_o \ is \ the \ initial \ velocity, \\and \ s_o \ is \ the \ initial \ height.\)

\(\displaystyle Hence, \ we \ have \ s(t) \ = \ h(t) \ = \ -16t^2+96t-128. \ s_o \ is \ 128 \ ft. \ below \ the \ earth's\)

\(\displaystyle surface, \ hence \ negative.\)

 

[alyren]

do i using polynomial factoring afterward?

 

[mmm4444bot]

do i using polynomial factoring afterward? After what? I'd factor it now, since all of the coefficients are multiples of -16.

The flare is visible above ground level.

Therefore, this exercise asks for the t-interval where h(t) > 0.

This interval is BETWEEN the t-intercepts.

Factoring the polynomial makes solving h(t) = 0 easy.

 

[dwilcox]

A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of 144 ft/sec, and the gorge is 288 ft deep, during what interval can the flare be seen?

 

[Dr.Peterson]

A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of 144 ft/sec, and the gorge is 288 ft deep, during what interval can the flare be seen?

Hijacking a 14-year-old thread doesn't absolve you of the need to follow the rules:

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