[SPLIT] Distance between rockets after 1 hr 36 mins

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baselramjet

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Mar 22, 2007
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This one has my head spinning :)

One rocket flies west from Nevada at 350 mph. A second rocket, shot at the same time from the same location as the first, flies southeast at 200mph. How far apart are the rockets after one hour and thirty-six minutes?

Edit (in reply to following post):
So I started out by multiplying each mph by 1.36
350*1.36= 476
200*1.36= 272

then I constructed a triangle

side a=272
side b=
side c= 476
angle A=
angle B= 45 degrees
angle C=

So I am assuming that to find the answer (How far apart are the rockets after one hour and thirty-six minutes?) I have to find what side c is?

Am I correct so far?
 
Construct a triangle.

Rocket A goes left from nevada
Rocket B is at a trajectory of 45 degrees apart from the direction of rocket A

use Distance = rate * time: This time is it much easier! Because both rocket distances (sides of triangle) are defined by d=rt

Apply some elementary trig principles

how far will they be apart?



I'm off to bed :) Have fun... this is little easier then the last one :)
Draw in all the data you have into a diagram until you cant draw any more.
 
Right triangles are easier; short cut: hypotenuse = a / SIN(A)
so 8000 / SIN(6) = 76534.1778....
 
ok...


So I started out by multiplying each mph by 1.36
350*1.36= 476
200*1.36= 272

then I constructed a triangle

side a=272
side b=
side c= 476
angle A=
angle B= 45 degrees
angle C=

So I am assuming that to find the answer (How far apart are the rockets after one hour and thirty-six minutes?) I have to find what side b is?

Am I correct so far?
So, using my calculator I came up with (rounded to the nearest hundreth)

side a=272
side b= 342.72
side c= 476
angle A= 34.14 degrees
angle B= 45 degrees
angle C= 100.86 degrees

So would the answer to:

How far apart are the rockets after one hour and thirty-six minutes?
342.72 miles?

how would I come to that without the calculator?
 
baselramjet said:
One rocket flies west from Nevada at 350 mph. A second rocket, shot at the same time from the same location as the first, flies southeast at 200mph. How far apart are the rockets after one hour and thirty-six minutes?
Click to expand...
One hour and 36 minutes is 1.6 hours.

The westerly flying rocket travels 350(1.6) = 560 miles while the southeasterly flying rocket travels 200(1.6) =320 miles in the 1.6 hours.

The angle between their two flight paths is 135º.

Using the Law of Cosines, the distance between the two rockets after 1.6 hours is

d = 560^2 + 320^2 - 2(560)320cos(135º) = 596.5 miles.
 
I thought you said southwest.. sorry. :)

Rocket A is flying horizontal to the ground going west....
Rocket B is flying south east = 90+45 = 135 degrees apart

Sorry for the initial confusion: TchrWill is correct.
 
Thank you, TchrWill!

If the triangle was

ANGLE A=
ANGLE B=135
ANGLE C=
side a=320
side b=
side c=560

the law of cosine be

b^2=a^2+c^2-2ac cosB

so,

b^2=320^2+560^2-2*320*560cos(135)

Right? (just trying to get this clear in my mind)

Ashley
 
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