Aplane has an airspeed of 111 km/h. it is flying on a bearing of 79 degrees while there is a 25 km/h wind out of the northeast (bearing 225 degrees). what are the ground speed and the bearing of the plane?

Ground Speed = 91 km/hr,   Bearing = 189°

Step-by-step explanation:

Step 1: Draw a picture (see attached) to determine the angle between the given vectors.  Notice that I moved the wind vector 180° so the head of the wind vector would line up with the tail of the plane vector. This created an angle of 34° between the plane and wind vectors. Why?

Step 2: Solve for the length of the resultant vector using Law of Cosines

c² = a² + b² - ab cos C

c² = (111)² + (25)² - (111)(25) cos 34°

c² = 12,946 - 4601

c² = 8345

c = 91

Ground speed is 91 km/hr

Step 3: Solve for the bearing of the resultant vector using Law of Sines

A = 9°

Reminder that we moved the wind vector 180° to create the resultant vector so we need to add 180° to our answer.

Bearing = A + 180°

              =  9° + 180°

              = 189°

45.3592

step-by-step explanation:

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.