A bird flies 2.0km south and then 1.5km 37∘ east of south. How far will it have to fly to get back to its original place if it flies in a straight line?
I tried to draw a drawing of this to illustrate it, but all I have is an obtuse triangle with a side of 2, a side of 1.5 and an angle of 37 (but when added with 90 becomes the obtuse angle). I guessed earlier and found out the answer was 3.3 since it was a multiple choice answer, but how do I get 3.3? I know that I'd use the law of vector addition but how am I supposed to apply it?? I can't just add 2 and 1.5 to get 3.3.
use the law of cosines. The distance z is
z^2 = 2^2 + 1.5^2 - 2*2*1.5 cos127°
z = 3.14 km
wait. But the correct answer is 3.3 so now I'm even more confused
also we never learned about the law of cosines in physics? I don't know anymore physics is messing me up
To find the distance the bird will have to fly to get back to its original place, we can use the law of vector addition. This law states that if we have two vectors, we can combine them by taking their magnitudes and directions into account.
In this case, we have a vector of 2.0 km to the south and a vector of 1.5 km 37 degrees east of south. To apply the law of vector addition, we can break down these vectors into their components.
The vector of 2.0 km to the south can be represented as a displacement of 2.0 km in the negative y-direction (y-component) since south is opposite to the positive y-axis.
The vector of 1.5 km 37 degrees east of south can be split into two components. The vertical component (y-component) is given by 1.5 km * sin(37 degrees), which gives us approximately 0.901 km in the negative y-direction. The horizontal component (x-component) is given by 1.5 km * cos(37 degrees), which works out to be approximately 1.199 km in the positive x-direction.
Now, we can add the x-components and y-components separately to get the resultant vector. Adding the x-components gives us 1.199 km, while adding the y-components gives us -2.901 km.
To find the magnitude (distance) of the resultant vector, we can use the Pythagorean theorem. The magnitude (d) is given by the square root of the sum of the squares of the x and y components:
d = sqrt((1.199 km)^2 + (-2.901 km)^2)
Evaluating this equation gives us d ≈ 3.206 km.
Therefore, the bird will have to fly approximately 3.206 km (or rounded to 3.2 km) to get back to its original place if it flies in a straight line.
To do the vector addition, just add the x- and y-components together to get the resultant.
Then get the length in the usual way.
Surely your text has examples of vector addition, and how to obtain the components of a vector.