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3 years ago

How can vectors be used in real life?

1 answer:

4 0

Using vectors can be troublesome for simple physics problems. however, when you move onto solving more difficult problems that have several variables, and the space you are dealing with is in three dimensions, using vectors is a necessity because it's not always possible to visualize the problem. but using vectors will give you a definitive answer.

few applications of vectors:
-predict the trajectory of airplanes and make sure that the airplane will not collide with some other airplane
-all simulations use vectors
-multivariable Calculus is pretty much based on vectors. without multivariable Calculus, it would have not been possible to compute many formulas.
-modeling the path a rocket will take, and supplying it the right amount of fuel so that it gets to the moon, or some other destination.

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The Trans-Siberian Railroad is the longest single railroad in the world. Starting in Moscow, the tracks stretch 9,354 km across

Lubov Fominskaja [6]

103.9 hours, if you never stopped for any reason.

4 0

4 years ago

ratelena [41]

Answer:

1.84 kJ (kilojoules)

Explanation:

A specific heat of 0.46 J/g Cº means that it takes 0.46 Joules of energy to raise the temperature of 1 gram of iron by 1 Cº.

If we want to heat 50 g of iron from 20° C to 100° C, we can make the following calculation:

Heat = (specific heat)*(mass)*(temp change)

Heat = (0.46 J/g Cº)*(50g)*(100° C - 20° C)

[Note how the units cancel to yield just Joules]

Heat = 1840 Joules, or 1.84 kJ

[Note that the number is positive: Energy is added to the system. If we used cold iron to cool 50g of 100° C water, the temperature change would be (Final - Initial) or (20° C - 100° C). The number is -1.84 kJ: the negative means heat was removed from the system (the iron).

8 0

2 years ago

A cube-shaped piece of copper has sides of 4cm each and it's density is

iris [78.8K]

Answer:

$64 cm^3$

Explanation:

<u>Density </u>

The density of a substance is the mass per unit volume. The density varies with temperature and pressure.

The formula to calculate the density of a substance of mass (m) and volume (V) is:

$\displaystyle \rho=\frac{m}{V}$

We have a cube-shaped piece of copper of 4 cm of side length. The volume of the piece is:

$V=(4\ cm)^3=64\ cm^3$

Surprisingly, no other magnitude is required, thus the answer is:

$\mathbf{64 cm^3}$

5 0

3 years ago

You pull on a spring whose spring constant is 22 N/m, and stretch it from its equilibrium length of 0.3 m to a length of 0.7 m.

Liono4ka [1.6K]

Answer:

W= 4.4 J

Explanation

Elastic potential energy theory

If we have a spring of constant K to which a force F that produces a Δx deformation is applied, we apply Hooke's law:

F=K*x Formula (1): The force F applied to the spring is proportional to the deformation x of the spring.

As the force is variable to calculate the work we define an average force

$F_{a} =\frac{F_{f}+F_{i} }{2}$ Formula (2)

Ff: final force

Fi: initial force

The work done on the spring is :

W = Fa*Δx

Fa : average force

Δx : displacement

$W = F_{a} (x_{f} -x_{i} )$ :Formula (3)

$x_{f}$ : final deformation

$x_{i}$ :initial deformation

Problem development

We calculate Ff and Fi , applying formula (1) :

$F_{f} = K*x_{f} =22\frac{N}{m} *0.7m =15.4N$

$F_{i} = K*x_{i} =22\frac{N}{m} *0.3m =6.6N$

We calculate average force applying formula (2):

$F_{a} =\frac{15.4N+6.2N}{2} = 11 N$

We calculate the work done on the spring applying formula (3) : :

W= 11N*(0.7m-0.3m) = 11N*0.4m=4.4 N*m = 4.4 Joule = 4.4 J

Work done in stages

Work is the change of elastic potential energy (ΔEp)

W=ΔEp

ΔEp= Epf-Epi

Epf= final potential energy

Epi=initial potential energy

$E_{pf} =\frac{1}{2} *k*x_{f}^{2}$

$E_{pi} =\frac{1}{2} *k*x_{i}^{2}$

$E_{pf} =\frac{1}{2} *22*0.7^{2} = 5.39 J$

$E_{pf} =\frac{1}{2} *22*0.3^{2} = 0.99 J$

W=ΔEp= 5.39 J-0.99 J = 4.4J

4 0

3 years ago

A projectile is launched with speed of 128 m/s, at an angle of 60° with the horizontal. After 2.0 s, what is the vertical compon

Natali5045456 [20]

Answer:

a) 91 m/s

b) 111 m/s

Explanation:

v = u + at

v = 128sin60 + (-9.8)(2.0) = 91.25125... m/s

v = √(vx² + vy²) = √((128cos60)² + 91.25125²) = 111.4575... m/s

5 0

3 years ago