an arctic flying to antarctica encounters a storm. The term changes direction to fly around the storn. if the tern flies 46 km at 15degrees south of east , 22 km at 13 degrees east of south , and finally 14km at 14 degrees west of south what is the tern's resultant displacement
There is an easy way to do this.
1) Convert all bearings from N as 000, clockwise.
add them as vectors:
R= (46Cos105+22Cos167+14Cos194)North + (46Sin105+22Sin167+14Sin194)East
do the math. check my angles.
ummmm dude i did that it came out like . something . like what do you mean convert N?. please explain
thankyou
To find the tern's resultant displacement, we can break down each leg of its journey into its north-south and east-west components. Then, we can add up all the north-south and east-west components separately to find the total north-south and east-west displacements. Finally, we can use these displacements to calculate the magnitude and direction of the resultant displacement using the Pythagorean theorem and trigonometry.
First, let's break down each leg of the journey into its north-south and east-west components:
For the first leg:
Distance = 46 km
Angle = 15 degrees south of east
The north-south (y-component) displacement can be found using the sine of the angle:
Displacement (north-south) = Distance * sin(angle) = 46 km * sin(15 degrees) = 11.92 km south
The east-west (x-component) displacement can be found using the cosine of the angle:
Displacement (east-west) = Distance * cos(angle) = 46 km * cos(15 degrees) = 44.61 km east
For the second leg:
Distance = 22 km
Angle = 13 degrees east of south
The north-south (y-component) displacement can be found using the cosine of the angle (since the angle is measured from the south):
Displacement (north-south) = Distance * cos(angle) = 22 km * cos(13 degrees) = 21.695 km south
The east-west (x-component) displacement can be found using the sine of the angle (since the angle is measured from the south):
Displacement (east-west) = Distance * sin(angle) = 22 km * sin(13 degrees) = 4.84 km east
For the third leg:
Distance = 14 km
Angle = 14 degrees west of south
The north-south (y-component) displacement can be found using the cosine of the angle (since the angle is measured from the south):
Displacement (north-south) = Distance * cos(angle) = 14 km * cos(14 degrees) = 13.325 km south
The east-west (x-component) displacement can be found using the sine of the angle (since the angle is measured from the south):
Displacement (east-west) = Distance * sin(angle) = 14 km * sin(14 degrees) = 3.13 km west
Now, let's add up all the north-south and east-west components separately to find the total north-south and east-west displacements:
Total north-south displacement = Displacement (north-south) from the first leg + Displacement (north-south) from the second leg + Displacement (north-south) from the third leg
= 11.92 km south + 21.695 km south + 13.325 km south = 46.94 km south
Total east-west displacement = Displacement (east-west) from the first leg + Displacement (east-west) from the second leg + Displacement (east-west) from the third leg
= 44.61 km east + 4.84 km east + (-3.13 km west) = 46.32 km east
Now, we can calculate the resultant displacement using the Pythagorean theorem:
Resultant displacement = sqrt((Total north-south displacement)^2 + (Total east-west displacement)^2)
= sqrt((46.94 km)^2 + (46.32 km)^2) = sqrt(4397.63 km^2 + 2143.89 km^2) = sqrt(6538.52 km^2) = 80.93 km
Finally, we can find the direction of the resultant displacement (angle with respect to the north) using trigonometry:
Direction = arctan(Total east-west displacement / Total north-south displacement)
= arctan(46.32 km east / 46.94 km south) = arctan(0.987)
≈ 46.48 degrees south of east
Therefore, the tern's resultant displacement is approximately 80.93 km at an angle of 46.48 degrees south of east.