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1 year ago

Find the lengths of each of the following vectors

Physics

1 answer:

Irina18 [472]1 year ago

3 0

Answer:

Explanation:

Generally, length of vector means the magnitude of the vector.

So, given a vector

R = a•i + b•j + c•k

Then, it magnitude can be caused using

|R|= √(a²+b²+c²)

So, applying this to each of the vector given.

(a) 2i + 4j + 3k

The length is

L = √(2²+4²+3²)

L = √(4+16+9)

L = √29

L = 5.385 unit

(b) 5i − 2j + k

Note that k means 1k

The length is

L = √(5²+(-2)²+1²)

Note that, -×- = +

L = √(25+4+1)

L = √30

L = 5.477 unit

Note that, since there is no component j implies that j component is 0

L = 2i + 0j - 1k

The length is

L = √(2²+0²+(-1)²)

L = √(4+0+1)

L = √5

L = 2.236 unit

(d) 5i

Same as above no is j-component and k-component

L = 5i + 0j + 0k

The length is

L = √(5²+0²+0²)

L = √(25+0+0)

L = √25

L = 5 unit

(e) 3i − 2j − k

The length is

L = √(3²+(-2)²+(-1)²)

L = √(9+4+1)

L = √14

L = 3.742 unit

(f) i + j + k

The length is

L = √(1²+1²+1²)

L = √(1+1+1)

L = √3

L = 1.7321 unit

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Calculate the number of moles in each of the following masses: 0.039 g of palladium 0.0073 kg of tantalum

marysya [2.9K]

Answer:

The number of moles of palladium and tantalum are 0.00037 mole and 0.0000404 mole respectively

Explanation:

Number of mole = reacting mass/molar mass

n = R.m/m.m......................... Equation 1

Where n = number of moles, R.m = reacting mass, m.m = molar mass.

For palladium,

R.m = 0.039 g and m.m = 106.42 g/mol

Substituting theses values into equation 1

n = 0.039/106.42

n = 0.00037 mole

For tantalum,

R.m = 0.0073 and m.m = 180.9 g/mol

Substituting these values into equation 1

n = 0.0073/180.9

n = 0.0000404 mole

Therefore the number of moles of palladium and tantalum are 0.00037 mole and 0.0000404 mole respectively

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2 years ago

Suppose that the current in the solenoid is i(t. within the solenoid, but far from its ends, what is the magnetic field b(t due

Mkey [24]

The answer is B(t) = constants x I(t)

Please take precaution on the point that it is an independent field of its radial position, if the point is measured well in the solenoid. (also the radial position is the axis of its symmetry)

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1 year ago

Read 2 more answers

A truck collides with a car on horizontal ground. At one moment during the collision, the magnitude of the acceleration of the t

Mice21 [21]

Answer:

The magnitude of the acceleration of the car is 35.53 m/s²

Explanation:

Given;

acceleration of the truck, $a_t$ = 12.7 m/s²

mass of the truck, $m_t$ = 2490 kg

mass of the car, $m_c$ = 890 kg

let the acceleration of the car at the moment they collided = $a_c$

Apply Newton's third law of motion;

Magnitude of force exerted by the truck = Magnitude of force exerted by the car.

The force exerted by the car occurs in the opposite direction.

$F_c = -F_t\\\\m_ca_c = -m_t a_t\\\\a_c =- \frac{m_ta_t}{m_c} \\\\a_c = -\frac{2490 \times 12.7}{890} \\\\a_c = - 35.53 \ m/s^2$

Therefore, the magnitude of the acceleration of the car is 35.53 m/s²

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2 years ago

Honeybees can see light in the ________ range of the electromagnetic spectrum.

konstantin123 [22]

Humans can see wavelengths in the visible part of the electromagnetic spectrum. That is the range of approximately 400 - 700 nm. Honeybees can see visible light and about 100 nm more in the ultraviolet part of the electromagnetic spectrum. That is approximately 300 - 700 nm.

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2 years ago

Suppose that now you want to make a scale model of the solar system using the same ball bearing to represent the sun. How far fr

Dahasolnce [82]

Answer:

d = 0.645 m (assuming a radius of the ball bearing of 3 mm)

Explanation:

The given information is:

The distance from the center of the sun to the center of the earth is 1.496x10¹¹m = $d_{e}$
The radius of the sun is 6.96x10⁸m = $r_{s}$

We need to assume a radius for the ball bearing, so suppose that the radius is 3 mm = $r_{b}$ .

First, we need to find how many times the radius of the sun is bigger respect to the radius of the ball bearing, which is given by the following equation:

$\frac{r_{s}}{r_{b}} = \frac{6.96\cdot 10^{8}m}{3\cdot 10^{-3}m} = 2.32\cdot 10^{11}$

Now, we can calculate the distance from the center of the sun to the center of the sphere representing the earth, $d_{s}$ :

[tex] d_{s} = \frac{d_{e}}{r_{s}/r_{b}} = \frac{1.496 \cdot 10^{11} m}{2.32\cdot 10^{11}} = 0.645 m

I hope it helps you!

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1 year ago