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Arada [10]
3 years ago
8

Vector A is added to a second vector B which has an x-component of 3 m and a y- component of -5 m. The resultant (A + B) is in t

he negative x direction and has a magnitude of 4 m. Find the magnitude and direction of A.
Physics
1 answer:
AlladinOne [14]3 years ago
8 0

Answer:

Explanation:

As B has a y component of -5, A must have a y component of 5 to have the result lie on the x axis.

As B has an x component of 3 and the result has an x component of -4, A must have an x component of -7

A = (-7, 5)

magnitude A = √(7² + 5²) = √74  ≈ 8.60

θ = arctan(y/x) = arctan(5/-7) ≈ 144.46° CCW from the positive x axis

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With 51 gallons of fuel in its tank, the airplane has a weight of 2390.7 pounds. What is the weight of the plane with 81 gallons
Shtirlitz [24]

Answer: 2561.7 pounds

Explanation:

If we assume the total weight of an airplane (in pounds units) as a <u>linear function</u> of the amount of fuel in its tank (in gallons) and we make a Weight vs amount of fuel graph, which resulting slope is 5.7, we can use the slope equation of the line:

m=\frac{Y-Y_{1}}{X-X_{1}}  (1)

Where:

m=5.7 is the slope of the line

Y_{1}=2390.7pounds is the airplane weight with  51 gallons of fuel in its tank (assuming we chose the Y axis for the airplane weight in the graph)

X_{1}=51gallons is the fuel in airplane's tank for a total weigth of 2390.7 pounds (assuming we chose the X axis for the a,ount of fuel in the tank in the graph)

This means we already have one point of the graph, which coordinate is:

(X_{1},Y_{1})=(51,2390.7)

Rewritting (1):

Y=m(X-X_{1})+Y_{1}  (2)

As Y is a function of X:

Y=f_{(X)}=m(X-X_{1})+Y_{1}  (3)

Substituting the known values:

f_{(X)}=5.7(X-51)+2390.7  (4)

f_{(X)}=5.7X-290.7+2390.7  (5)

f_{(X)}=5.7X+2100  (6)

Now, evaluating this function when X=81 (talking about the 81 gallons of fuel in the tank):

f_{(81)}=5.7(81)+2100  (7)

f_{(81)}=2561.7  (8)   This means the weight of the plane when it has 81 gallons of fuel in its tank is 2561.7 pounds.

3 0
3 years ago
Taigas, tundra and tropical rainforests share what common abiotic component?
e-lub [12.9K]

Answer:

water

Explanation:

hope this helps

6 0
3 years ago
A hollow conductor is positively charged. Asmall uncharged metal ball is lowered by a silk thread through asmall opening in the
dimulka [17.4K]

Answer:

Explanation:

According to the property of a conductor, the entire charge will reside on the outer surface of the conductor, there is no charge on the inner side of the conductor. As the uncharged metal ball touches the inner surface of the conductor, it does not attain any charge as the inner side of the conductor has no charge.

So option (c) is correct.

8 0
3 years ago
Write a method which prevents ice from melting quickly.​
Gnom [1K]

Answer:

blocks of ice are usually covered with cloth or sawdust while being stored

4 0
3 years ago
A thin lens with a focal length of 6.0 cm is used as a simple magnifier by (a) what angular magnification is obtainable with the
Serhud [2]

Answer:

4.167

4.83871 cm

Explanation:

u = Object distance

v = Image distance = 25 cm

f = Focal length = 6 cm

Angular magnification is given by

m=\frac{25}{f}\\\Rightarrow m=\frac{25}{6}\\\Rightarrow m=4.167

The angular magnification of the lens is 4.167

Lens equation

\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\\\Rightarrow \frac{1}{6}=\frac{1}{u}+\frac{1}{-25}\\\Rightarrow \frac{1}{6}+\frac{1}{25}=\frac{1}{u}\\\Rightarrow \frac{1}{u}=\frac{31}{150}\\\Rightarrow u=4.83871\ cm

The closest distance by which the object can be examined is 4.83871 cm

5 0
3 years ago
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