Mathematics, 05.10.2019 19:30 naomicervero

You're flying from joint base lewis-mcchord (jblm) to an undisclosed location 125 km south and 135 km east. mt. rainier is located approximately 56 km east and 40 km south of jblm. if you are flying at a constant speed of 800 km/hr, how long after you depart jblm will you be the closest to mt. rainier?
convert hours into minutes in the final solution.

Answers: 1

Show answers

Answers

Answer from: BM213

5.12 minutes ≈ 5 minutes 7.2 seconds

Step-by-step explanation:

The flight path of the airplane is along the line ...

y = -125/135x = -25/27x

The perpendicular line through Mt. Rainier's location is ...

y = 27/25(x -56) -40

In standard form, these two equations are ...

25x +27y = 027x -25y = 2512

The point of closest approach has the coordinates that are the solution to these two equations:

(x, y) = (33912/677, 31400/677)

The distance d from the origin to this point is given by the Pythagorean theorem (distance formula) as ...

d = 1256√(2/677) . . . . . km

This distance can be converted to time using the speed of the airplane:

$(1256\sqrt{\dfrac{2}{677}}\,km)\times \dfrac{60\,min}{800\,km}=94.2\sqrt{\dfrac{2}{677}}\,min\approx 5.120019\,min$

5.12 minutes after departing JBLM you will be closest to Mt. Rainier.

_____

The attached graph shows the geometry of the problem.

You're flying from joint base lewis-mcchord (jblm) to an undisclosed location 125 km south and 135 k

Answer from: blackordermember

The closest distance from a point to a line is its perpendicular distance to the line

The time it would take to be closest to Mt Rainier, is approximately 5.12 minutes

The reason why the value is correct is given as follows:

The given parameters are;

The direction of flight = 125km south and 135 km east

The location of Mt. Retainer = 56 km east and 40 km south of JBLM

The speed of flight = 800 km/hr

The slope of the travel path, m, is given as follows;

$m = -\dfrac{125}{135} = -\dfrac{25}{27}$

The equation of the path is therefore;

$y + 125 = -\dfrac{25}{27} \times (x - 135)$

$y = -\dfrac{25}{27} \times (x - 135) - 125$

The required slope for the perpendicular distance from the travel path to the Mt Rainier, m', is therefore;

$m' = -\dfrac{1}{m}$

Which gives;

$m' = -\dfrac{1}{-\dfrac{25}{27}} = \dfrac{27}{25}$

The equation of the line is therefore;

$y + 40 = \dfrac{27}{25} \times (x - 56)$

$y = \dfrac{27}{25} \times (x - 56) - 40$

The coordinates of the point where the two lines meet is therefore;

$\dfrac{27}{25} \times (x - 56) - 40 = -\dfrac{25}{27} \times (x - 135) - 125$

Solving with a graphing calculator gives;

x ≈ 50.09

y ≈ -46.38

The magnitude of the distance in km is, d = $\sqrt{(-46.38^2 + 50.09^2)} \approx 68.267$

The time it will take to be closest to Mt. Rainier, t, is given as follows;

$t \approx \dfrac{68.267 \, km}{800 \, km/hour} \approx 8.53 \times 10^{-2} \, hour$

The time it would take to get closest to Mt Rainier, t ≈ 8.53 × 10⁻² hours

$The \ time \ in \ minutes, \, t = 8.53 \times 10^{-2} \ hour\times \dfrac{60 \, min}{hour} \approx \underline {5.12 \ minutes}$

Time it would take to be closest to Mt Rainier in minutes, t ≈ 5.12 minutes

Learn more about distance from a line to a point here:

link

Answer from: Quest

Wednesday1.) < 2.) 1961015.)6.486.)68.761 can be rounded up to 69i can't truly see the rest and my next comment will be thursday
Me with wendsday and thursday questions going straight down show work you

Me with wendsday and thursday questions going straight down show work you

Answer from: Quest

i use my brain for prombles like this maybe you could try it

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 23:00

Of the 304 people who attended a school play, 5/8 were students. how many of the people who attended were students.

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

Savannah had 40 iris blooms last year this year she had 15% more iris blooms how many more hours blooms did savannah have this year

Answers: 1

Answer

Mathematics, 22.06.2019 01:30

A23 – year – old male buys 100/300/100 liability insurance, collision insurance with a $100 deductible, and comprehensive insurance with a $250 deductible? what is his total annual premium? (a) $1142.00 (b) $1765.45 (c) $1770.10 (d) $1785.25

Answers: 2

Answer

Mathematics, 22.06.2019 03:30

The distance between a football fsaid and a parking lot is 135 feet. what is that length in yards? 2 mickey needs to cut pieces of ribbon that are each 1 meter long to tie onto balloons. if he has 8 pieces of ribbon that are each 1 dekameter long, how many 1-meter pieces of ribbon can he cut? show work

Answers: 1

Answer

You know the right answer?

You're flying from joint base lewis-mcchord (jblm) to an undisclosed location 125 km south and 135 k...

Questions

Mathematics, 23.01.2022 22:10

Which expression gives the area of the triangle shown below

Mathematics, 23.01.2022 22:20

What are the values of x in the equation x2 – 6x + 9 = 25? x = –2 or x = 8 x = –1 or x = –11 x = 1 or x = 11 x = 2 or x = –8...