+0  
 
0
827
3
avatar+91 

http://i68.tinypic.com/5mn1ci.jpg

 Nov 15, 2016

Best Answer 

 #2
avatar+129899 
+10

We can get the answer to 25 by first finding the distance,d, the plane has traveled for 10:24 to 11PM.....since it has been flying for 36 min...we have that 

 

d/36 = 17.91/5 

 

d =36*17.91/ 5 ≈ 128.952 miles

 

And we can find the (x, y)  coordinates of its terminal point as follows

 

[ 120cos(280) + 128.952cos(69.28) , 120sin(280) + 128.952sin(69.28)  ]    →  x = 66.4612 and y = 2.43453

 

So....the new trminal point is [ 66.4612, 2.43453]

 

And the distance  [from (0,0) ]  is given  by ..... sqrt   [  66.4612^2  +  2.43453^2 ]  ≈ 66.5058 mi ≈ 67 miles   [rounded]

 

And the bearing is given by   [ 90 - arctan(2.43453/66.4612) ] °   =  [90 - 2.098]° ≈ 87.902° = 88°  [rounded]

 

So...the new heading (bearing)  is     88° at  67 miles

 

 

 

cool cool cool

 Nov 15, 2016
 #1
avatar+129899 
+10

We can use the Law of Cosines to get tthe answer to 23

 

We need to find the distance, x, traveled by theplane in  5 minutes....note that the angle betewwn the vectors = 5°

 

So...we have

 

x^2 = 120^2 + 105^2 - 2(120)(105)cos(5°)

 

x = sqrt [ 120^2 + 105^2 - 2(120)(105)cos(5°)]  ≈  17.91 miles

 

Then...if it traveled  17.91 miles in 5 minutes...it would be traveling at  17.91 * 12  ≈  214.92mph ≈  215 mph

 

To get the answer to 24,    let us find the slope between the coordinates  end points of the vectors...we have

 

[ 120cos(280), 120 sin(280)]     and ( [ 105cos(285), 105sin(285) ]  = 

 

[ 105sin(285) - 120sin(280) ] / [105cos(285) - 120cos(280)]  ≈ 2.643

 

Using the tangent inverse of this to find the angle of the slope, we have arctan(2.643)  ≈ 69.28°

 

And subtracting this from 90 will give us a heading of about 90 - 69.28 = 20.72° ≈  21°

 

[I'm still thinking about the answer to 25 ] 

 

 

 

cool cool cool

 Nov 15, 2016
 #3
avatar+118687 
+5

Q24 am just using CPhill's method of putting it all on a grid.

 

 

 

 

so

\(gradient=\frac{-105sin75--120cos10}{105cos75-120sin10}\\ gradient=\frac{-105sin75+120cos10}{105cos75-120sin10}\\ gradient=2.64\\ tan\theta=2.64\\ \theta\approx 69.28\\ \)

CPhill did this ths fast way  LOL

 

Now 69.28 degrees is the angle between the positive x axis and the direction the plane is flying

but the x axis is in the due east direction whereas direction is taken from the due north direction so

the plane is flying on a bearing of   90-69.28 = 20.72 degrees

 

So just like CPhill found the plane is flying with a bearing of approximately 21 degrees.

Melody  Nov 17, 2016
 #2
avatar+129899 
+10
Best Answer

We can get the answer to 25 by first finding the distance,d, the plane has traveled for 10:24 to 11PM.....since it has been flying for 36 min...we have that 

 

d/36 = 17.91/5 

 

d =36*17.91/ 5 ≈ 128.952 miles

 

And we can find the (x, y)  coordinates of its terminal point as follows

 

[ 120cos(280) + 128.952cos(69.28) , 120sin(280) + 128.952sin(69.28)  ]    →  x = 66.4612 and y = 2.43453

 

So....the new trminal point is [ 66.4612, 2.43453]

 

And the distance  [from (0,0) ]  is given  by ..... sqrt   [  66.4612^2  +  2.43453^2 ]  ≈ 66.5058 mi ≈ 67 miles   [rounded]

 

And the bearing is given by   [ 90 - arctan(2.43453/66.4612) ] °   =  [90 - 2.098]° ≈ 87.902° = 88°  [rounded]

 

So...the new heading (bearing)  is     88° at  67 miles

 

 

 

cool cool cool

CPhill Nov 15, 2016

1 Online Users