Respuesta :
Answer:
d= 64.7 km
[tex]\theta = 40.9^{o}[/tex]
displacement vector[tex]=r_xi + r_yj = 48.9i + 42.4j[/tex]
Explanation:
total distance = 40 + 30 = 70 km
during 1st flight
[tex]r_1 x = 40*cos60[/tex]
[tex]r_1 x = 20 km[/tex]
[tex]r_1 y = 40*sin60[/tex]
[tex]r_1 y = 34.64 km[/tex]
during 2nd flight
[tex]r_2 x = 30*cos15[/tex]
[tex]r_2 x = 28.9 km[/tex]
[tex]r_2 y = 30*sin15[/tex]
[tex]r_2 y = 7.76 km[/tex]
the two component of r are:
[tex]r_x = r_1x + r_2x = 20 + 28.9 = 48.9 km[/tex]
[tex]r_y = r_1y + r_2y = 34.64 + 7.76 = 42.4 km[/tex]
Geographical Direction [tex]\theta = tan^{-1}\frac{r_y}{r_x}
[tex]\theta = 40.9^{o}[/tex]
Displacement d[tex] = \sqrt{r_x^2 + r_y^2}[/tex]
[tex] d = \sqrt{48.9^2+42.4^2} = 64.7 km[/tex]
d= 64.7 km
displacement vector[tex]=r_xi + r_yj = 48.9i + 42.4j[/tex]
Displacement vector for small plane flies in north of east direction tells the distance and direction of it from initial position.
- a) Total distance the plane covers from the starting point is 64.7
- b) The geographic direction of its displacement vector is in the 40.9 degrees north of east.
- c) The displacement vector is,
[tex]r_xi+r_yi=48.9i+42.4j[/tex]
What is displacement vector?
Displacement vector is used to known the change of position of a particle along with its direction.
Given information-
The small plane flies 40.0 km in a direction 60° north of east.
The small plane flies 30.0 km in a direction 15° north of east.
- a) Total distance the plane covers from the starting point-
The total distance in the horizontal plane covered by the small plane is,
[tex]r_x=40\cos(60)+30\cos(15)\\r_x=48.9\rm km[/tex]
The total distance in the vertical plane covered by the small plane is,
[tex]r_x=40\sin(60)+30\sin(15)\\r_x=42.4\rm km[/tex]
Thus total distance the plane covers from the starting point-
[tex]d=\sqrt{r_x^2+r_y^2}\\d=\sqrt{48.9^2+42.4^2}\\d=64.7\rm km[/tex]
Hence, the total distance the plane covers from the starting point is 64.7 km.
- b) The geographic direction of its displacement vector.
The geographic direction of the displacement vector can be given as,
[tex]\tan\theta=\dfrac{r_x}{r_y}[/tex]
Put the values,
[tex]\theta=\tan^{-1}(\dfrac{42.4}{48.9})\\\theta=40.9^o[/tex]
Hence, the geographic direction of its displacement vector is in the 40.9 degrees north of east.
- c) The displacement vector-
Displacement vector can be given as,
[tex]r_xi+r_yi=48.9i+42.4j[/tex]
Hence,
- a) Total distance the plane covers from the starting point is 64.7
- b) The geographic direction of its displacement vector is in the 40.9 degrees north of east.
- c) The displacement vector is,
- [tex]r_xi+r_yi=48.9i+42.4j[/tex]
Learn more about the displacement vector here;
https://brainly.com/question/13416288
