If a substance cannot be separated by physical means or chemical means, it is ___________.
2 answers:
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Answer:
a) R = 2.5 mi b) To return to your case you must walk in the opposite direction or θ = 98º
This is 8º north west
Explanation:
This is a distance exercise with vectors the best way to work these is to decompose the vectors and perform the sum on each axis separately
To use the Cartesian system all angles must be measured from the positive side of the x-axis or the signs of the components must be assigned manually depending on the quadrant where they are.
First vector A = 2 to 20º north west
Measured from the positive x axis is θ = 180 -20 = 160º
We use trigonometry to find the components
Cos 20 = Aₓ / A
sin 20 = / A
Aₓ = A cos 160 = 2 cos 160
= A sin160 = 2 sin160
Aₓ = -1,879 mi
= 0.684 mi
Second vector B = 4 mi 10º west of the south
Angle θ = 270 - 10 = 260º
cos 2600 = Bₓ / B
sin 260 = / B
Bₓ = B cos 260
= B sin 260
Bₓ = 4 cos 260
= 4 sin 260
Bₓ = -0.6946mi
= - 3,939 mi
Third vector C = 3 mi to 15 north east
cos 15 = Cₓ / C
sin15 = / C
Cₓ = C cos 15
= C sin15
Cₓ = 3 cos 15
= 3 sin 15
Cₓ = 2,898 mi
= 0.7765 mi
Now we can find the final position of the person
X = Aₓ + Bₓ + Cₓ
X = -1.879 -0.6949 + 2.898
X = 0.3241 mi
Y = +
+
Y = 0.684 - 3.939 +0.7765
Y = -2.4785 mi
a) We use Pythagoras' theorem
R = √ (x2 + y2)
R = √ (0.3241 2 + (-2.4785) 2)
R = 2.4996 mi
R = 2.5 mi
b) let's use trigonometry
Tan θ = y / x
Tanθ = -2.4785 / 0.3241
θ = tan⁻¹ (-7,647)
θ = -82
Measured from the positive side of the x axis is Te = 360 - 82 = 278º
(90-82) south east
To return to your case you must walk in the opposite direction or Te = 98º
This is 8º north west
The total average velocity 
(I assume west as positive direction) is given by the total displacement, S, divided by the total time taken, t:
where:
-The total displacement S is the algebraic sum of the displacement in the first part of the motion (
, due west) and of the displacement in the second part of the motion (
, due east).
-The total time taken t is the time taken for the first part of the motion,
, and the time taken for the second part of the motion, 
. can be found by using the average velocity and the displacement of the first part:
, instead, can be written as 
, where 
is the average velocity of the second part of the motion (with a negative sign, since it is due east).
Therefore, we can rewrite the initial equation as:
And by solving it, we find the displacement in the second part of the motion (i.e. how far did the backpacker move east):
where:
-The total displacement S is the algebraic sum of the displacement in the first part of the motion (
-The total time taken t is the time taken for the first part of the motion,
Therefore, we can rewrite the initial equation as:
And by solving it, we find the displacement in the second part of the motion (i.e. how far did the backpacker move east):
Answer:
Time = 0.55 s
Height = 8.3 m
Explanation:
The ball is dropped and therefore has an initial velocity of 0. Its acceleration, g, is directed downward in the same direction as its displacement, .
The dart is thrown up in which case acceleration, g, acts downward in an opposite direction to its displacement, . Both collide after travelling for a time period, t. Let the height of the dart from the ground at collision be
and the distance travelled by the ball measured from the top be
.
It follows that .
Applying the equation of motion to each body (h = v_0t + 0.5at^2),
Ball:
(since
.)
Dart:
(the acceleration is opposite to the displacement, hence the negative sign)
But
The height of the collision is the height of the dart above the ground, .