Answer:
- < 25 m/s
- triangle inequality
- between north and east
- 45° < angle < 60°
Explanation:
(a) Just as one-dimensional numbers add on a number line by putting them end-to-end, so two-dimensional numbers add on a coordinate plane the same way.
Here, we choose to let the positive y-axis represent North, and the positive x-axis, East. This is the way a map is conventionally oriented. The velocity of the plane is represented by a vector pointing north (up). Its length represents the magnitude of the velocity. Likewise, the wind is represented by a vector of length 15 pointing east (right). The sum of these is the hypotenuse of the triangle they form.
The magnitude of the sum can be found here using the Pythagorean theorem, but for the purpose of this question, you're not asked to find that.
Instead, you're asked to estimate whether it is more or less than 25 (m/s).
Your knowledge of the triangle inequality will tell you that the hypotenuse (resultant) must be shorter than the sum of the lengths of the sides of the triangle, hence must be less than 10+15 = 25.
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(b) The triangle inequality says the resultant is less than the sum of the other two sides of the triangle.
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(c) Since the wind is blowing the plane toward the east, but the plane is traveling toward the north, the resulting direction is somewhere between north and east.
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(d) "Somewhere between north and east" can be expressed as the inequality ...
0° < angle < 90°
First find the time it takes to hit the sand t
using s=1/2 g t^2
t^2= 8/9.8= 0.82 seconds
This means the sand was s = 8 * 0.82 = 6.5m away
The horizontal speed stays constant at 8 m/s
The vertical speed =.82 * 9.8 = 8.0 m/s
As the two velocities are equal the angle must be 45 degrees to the horizontal
Independent- nose of the airplane
dependent - paper clips
control - how many paper clips
In order to solve this problem all you have to do is multiply 15 by 3.5 which equals 52.5
So the answer is D. 52.5 miles!
Aster's final position from her initial position is 63 m approximately. She will head north west direction to return to her initial position
<h3>
What is Displacement ?</h3>
Displacement is the distance travelled in a specific direction. It is a vector quantity.
Given that a person walks first 70 m in the direction 37° north of east, and then walks 82 m in the direction 20° south of east, and finally walks 28 m in the direction 30° west of north.
a) Let P be the Aster's final position from her initial position?
We can use bearing by using Cosine formula to solve this question.
P² = 70² + 82² - 2 × 70 × 82 cos 73
P² = 4900 + 6724 - 11480 cos 73
P² = 11624 - 3356.43
P² = 8267.57
P = √8267.57
P = 90.9 m
P = 90.9 - 28
P = 62.9 m
We can get the angle by using Sine rule
82/ sin Ф = 90.9 / sin 73
sin Ф = 0.8627
Ф = 
(0.8627)
Ф = 59.6°
Ф = 60°
b) She will head north west direction to return to her initial position
Learn more about Displacement here: brainly.com/question/2109763
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