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3 years ago

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The displacement vector from your house to the library is 740 m long, pointing 40 ∘ north of east. Part A What are the x-compone

nt (x-axis is directed from west to east) of this displacement vector?

1 answer:

Ilia_Sergeevich [38]3 years ago

4 0

The horizontal component of the displacement is 566.9 m

Explanation:

The horizontal (x-) and vertical (y-) components of a vector on the Cartesian plane can be found as follows:

$v_x = v cos \theta$

$v_y = v sin \theta$

where

v is the magnitude of the vector

$\theta$ is the angle representing the direction of the vector, measured as above the x-axis.

In this problem, we have:

v = 740 m (magnitude of the vector)

$\theta=40^{\circ}$ (direction of the vector)

Therefore, the two components are

$v_x = (740)(cos 40)=566.9 m$

$v_y = (740)(sin 40)=475.7 m$

Learn more about vector components:

brainly.com/question/2678571

#LearnwithBrainly

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Two go-carts, A and B, race each other around a 1.0 track. Go-cart A travels at a constant speed of 20.0 /. Go-cart B accelerate

maria [59]

Complete Question

Q. Two go-carts, A and B, race each other around a 1.0km track. Go-cart A travels at a constant speed of 20m/s. Go-cart B accelerates uniformly from rest at a rate of 0.333m/s^2. Which go-cart wins the race and by how much time?

Answer:

Go-cart A is faster

Explanation:

From the question we are told that

The length of the track is $l = 1.0 \ km = 1000 \ m$

The speed of A is $v__{A}} = 20 \ m/s$

The uniform acceleration of B is $a__{B}} = 0.333 \ m/s^2$

Generally the time taken by go-cart A is mathematically represented as

$t__{A}} = \frac{l}{v__{A}}}$

=> $t__{A}} = \frac{1000}{20}$

=> $t__{A}} = 50 \ s$

Generally from kinematic equation we can evaluate the time taken by go-cart B as

$l = ut__{B}} + \frac{1}{2} a__{B}} * t__{B}}^2$

given that go-cart B starts from rest u = 0 m/s

So

$1000 = 0 *t__{B}} + \frac{1}{2} * 0.333 * t__{B}}^2$

=> $1000 = 0 *t__{B}} + \frac{1}{2} 0.333 * t__{B}}^2$

=> $t__{B}} = 77.5 \ seconds$

Comparing $t__{A}} \ and \ t__{B}}$ we see that $t__{A}}$ is smaller so go-cart A is faster

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2 years ago

A hot-air balloon has a volume of 440 × 10^3 ^3. Calculate the buoyant force that the surrounding cold air exerts on the balloon

siniylev [52]

Answer:

Explanation:

Given that,

The volume of the balloon is

V = 440 × 10³ m³

Buoyant force F?

Given the density of the surrounding to be 2.58 kg/m³

ρ = 2.58 kg/m³

The buoyant force is the weight of water displaced and it is calculated using

F_b = ρVg

Where

F_b is buoyant force

ρ is density

V is the volume of the liquid displace.

g is the acceleration due to gravity

Then,

F_b = ρVg

F_b = 2.58 × 440 × 10³ × 9.81

F_b = 1.1 × 10^7 N

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3 years ago

Write a difference between force and work?

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Answer:

force is a derived quantity

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Explanation:

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2 years ago

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A mass of 0.5 kg hangs motionless from a vertical spring whose length is 1.10 m and whose unstretched length is 0.50 m. Next the

ser-zykov [4K]

Answer:

The maximum length during the motion is $L_{max} = 1.45m$

Explanation:

From the question we are told that

The mass is $m =0.5 kg$

The vertical spring length is $L = 1.10m$

The unstretched length is $L_{un} = 1.30m$

The initial speed is $v_i = 1.3m/s$

The new length of the spring $L_{new} = 1.30 m$

The spring constant k is mathematically represented as

$k = -\frac{F}{y}$

Where F is the force applied $= m * g = 0.5 * 9.8=4.9N$

y is the difference in weight which is $=1.10-0.50=0.6m$

The negative sign is because the displacement of the spring (i.e its extension occurs against the force F)

Now substituting values accordingly

$k = \frac{4.9}{0.6}$

$= 8.17 N/m$

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where D is this the is the displacement

Since Energy is conserved the total elastic potential energy would be

$E_T = initial \ elastic\ potential \ energy + kinetic \ energy$

$E_T = \frac{1}{2} k D_{max}^2 = \frac{1}{2} k D^2 + \frac{1}{2} mv^2$

Substituting value accordingly

$\frac{1}{2} *8.17 *D_{max}^2 =\frac{1}{2} * 8.17*(1.30 - 0.50)^2 + \frac{1}{2} * 0.5 *1.30^2$

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So to obtain total length we would add the unstretched length

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Explanation:

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