I need help with this please

Answer:

6.7 seconds

Explanation:

d=(1/2)at^2

equation

1000=(1/2)45t^2.

substitute

2000=45t^2.

multiply by 2 for both sides

44.44=t^2.

divide both sides by 45

6.7=t

take the square root of both sides

Answer:

v = 1.74 m/s

Explanation:

Given that,

Diameter of a circular track, d = 100 m

Distance covered for the 4 laps,

[tex]D=4\pi d\\\\D=4\pi \times 100\\\\D=1256.63\ m[/tex]

Time, t = 12 minutes = 720 s

We need to find the velocity of the peter. It can be calculated as follows :

[tex]v=\dfrac{D}{t}\\\\v=\dfrac{1256.63\ m}{720\ s}\\\\v=1.74\ m/s[/tex]

So, the speed is running with a velocity of 1.74 m/s.

Peter is running at 1.7453 m/sec.

Given to us,

Diameter of the circular track, D = 100 meters,

Number of laps Peter run, L = 4 laps,

Time taken by Peter, t = 12 minutes,

1 lap = circumference of the circle,

4 laps = 4 x circumference of the circle,

As we know, the circumference of a circle is given by πD.

So, 4 laps = 4 x circumference of the circle,

[tex]\begin{aligned}4 laps &= 4\times \pi \times D\\&= 4 \times \pi \times 100\\& = 1,256.6370\ meters\\\end{aligned}[/tex]

Also, we know that 1 minute has 60 sec.

so, 4 minutes = (4 x 60) seconds

Further, speed is given [tex]\bold{(\dfrac{Distance}{Time} )}[/tex]

Thus,

[tex]\begin{aligned}speed &= \dfrac{Distance\ coverd\ by\ Peter}{Time\ taken\ by\ Peter}\\&=\dfrac{1,256.6370}{12\times 60}\\&=1.7453\ m/sec \end{aligned}[/tex]

Hence, Peter is running at 1.7453 m/sec.

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Answer:

Explanation:

Hydrogen fluoride (HF) is an ionic/electrovalent compound that dissociates into ions when dissolved in water. It's dissociation is as seen below

HF ⇄ H⁺ + F⁻

There is a transfer of electron from the hydrogen atom which produces the hydrogen ion (H⁺), while the fluorine atom receives the donated ion to become negatively charged (F⁻). The amount of charge in one electron is generally given as 1.602 × 10⁻¹⁹ coloumbs.

The required value of effective charge on HF molecule, due to H and F is  1.602 × 10⁻¹⁹ Coulombs.

The given problem is based on the concept of effective charges. The net positive charge carried out by the electrons of atomic species, after forming a polyelectronic atom  is known as Effective charge.

As per the given problem, the Hydrogen fluoride (HF) is an ionic/electrovalent compound that dissociates into ions when dissolved in water. It's dissociation is given as,

HF ⇄ H⁺ + F⁻

There is a transfer of electron from the hydrogen atom which produces the hydrogen ion (H⁺), while the fluorine atom receives the donated ion to become negatively charged (F⁻). The amount of charge in one electron is generally given as 1.602 × 10⁻¹⁹ Coulombs.

Thus, we can conclude that the required value of effective charge on HF molecule, due to H and F is 1.602 × 10⁻¹⁹ Coulombs.

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Answer:

use special filters on the telescope

Explanation:

Assuming you have access to a very high-grade telescope you would need to use special filters on the telescope that allows you to view the star's color spectrum. The color spectrum represents different levels of heat that a star is generating. This spectrum ranges from red to blue. Therefore in order to calculate the surface temperature, you would need to apply both a blue and red filter onto the telescope. Once you have these measurements you would need to compare them in order to pinpoint the correct variation of color which would give a close enough estimate of the surface temperature of the star.

Answer:

A. decantation and screening

Explanation:

Decantation is the one of the process of separating the mixture. In this process the precipitated liquid is separated from the solid. According to the given instruction for the recipe, the fat which is in liquid state is separated from meat. In the process of screening, more liquid is separated by placing the mixture on the screen. Here, the gravity plays an important role for the process of separation.  

Answer:

a

Explanation:

Answer:

Explanation:

If the ray were not deviated, it would travel straight through the mirror. Due to the mirror, the incident ray is reflected at 30°. The ray travels 30° + 30° = 60°. The angle of deviation is 180° - 60° = 120°.

Explanation:

The two mirrors inclined to each other formed the first two images with are of the same size as the object while the third mirror is produced from the intersection of rays that emanated during the production of the first two images to produce a third image which is smaller than the object and there making the total number of images to be 3.

Hence this mirrors produces 3 images due to the third image formed from the intersection of the rays that produces the first two images.

The formula that relates the image produced by inclined mirror and the angle of inclination is expressed as:

number of images n = 360/θ - 1

θ is the angle of inclination of the two mirrors

n is the number of images

If the mirrors are inclined at right angles, then θ = 90°

Substitute into the formula;

n = 360/90 -1

n = 36/9 -1

n = 4-1

n = 3

This question is incomplete, the complete question is;

For this force system the equivalent system at P is ___________

A) FRP = 40 lb (along +x-dir.) and MRP = +60 ft.lb

B) FRP = 0 lb and MRP = +30 ft.lb

C) FRP 30 lb (along +y-dir.) and MRP  = -30 ft.lb

D) FRP 40 lb (along +x-dir.) and MRP = +30 ft.lb

Answer:

D) FRP 40 lb (along +x-dir.) and MRP = +30 ft.lb

Explanation:

From the figure in the image i uploaded along this answer;

FRP = ( 40 lb i + 30 lb j ) + [30 lb (-j)]

Where i  and j are the unit vectors along X & Y axis respectively.

So, FRP = 40 lb i

that is,  FRP = 40 lb along +X direction

MRP = [ 30 lb x ( 1 ' + 1' ) ] +( -30 lb x 1 ' )

= (30 lb x 2 ' )- 30 lb ft

= 60 lb ft - 30 lb ft

= 30 lb ft

Therefore option(D) is correct    

Answer:

A

Explanation:

hope this helps

Answer:

the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment.

Explanation:

Answer:

F=1.3x10^-2N

Explanation:

Fe= k(6x10^-7C)^2/(0.5)^2

Electrical force of attraction between the balloons is F=1.3x10^-2N

The electric force of attraction between two balloons should be F=1.3x10^-2N.

Since The charge on the balloons is 6.0 x 10-7 C and they are separated by a distance of 0.50 m.

So, here the electric force is

Fe= k(6x10^-7C)^2/(0.5)^2

F=1.3x10^-2N

hence, The electric force of attraction between two balloons should be F=1.3x10^-2N.

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Answer:

10 seconds

Explanation:

As it starts from rest, then u=0

and by III rd equation of motion:

Answer:

-z

Explanation:

The force on a moving charge due to a magnetic field follows the right hand rule, so a positive charge, experiencing a magnetic deflection in the -y direction, while it moves in the direction of the x-axis, will do it  due to a magnetic field pointing in the +z direction.

As the electron has a negative charge, the magnetic field will point in the opposite direction, i.e., in the -z direction.

Answer:

1. p = 562.3 kg*m/s

2. F = 142.7 N

Explanation:

1. The linear impulse (p) is given by:

[tex] p = mv [/tex]

Where:

m: is the passenger's mass = 73.7 kg

v: is the speed = 7.63 m/s

[tex] p = mv = 73.7 kg*7.63 m/s = 562.3 kg*m/s [/tex]

Hence, the magnitude of the linear impulse experienced by a passenger is 562.3 kg*m/s.

2. The average force can be calculated using the following equation:

[tex] F = \frac{m(v_{f} - v_{0})}{t} = \frac{73.7 kg(7.63 m/s - 0)}{3.94 s} = 142.7 N [/tex]  

Therefore, the average force experienced by the passenger is 142.7 N.

I hope it helps you!

Answer:

1.3 m/s

Explanation:

It is given that,

Mass of bird A, [tex]m_A=2.2\ kg[/tex]

Mass of bird B, [tex]m_B=1.7\ kg[/tex]

Initial speed of bird A is 0 as it was at rest

Initial speed of bird B is 3 m/s

We need to find the velocity of the center of mass for this system of two birds. Let it is V. so,

[tex]v_{cm}=\dfrac{m_Au_A+m_Bu_B}{m_A+m_B}\\\\v_{cm}=\dfrac{2.2\times 0+1.7\times 3}{2.2+1.7}\\\\v_{cm}=1.3\ m/s[/tex]

So, the center of mass for this system is 1.3 m/s.

Complete Question

How many turns are in its secondary coil, if its input voltage is 120 V and the primary coil has 210 turns.

The output from the secondary coil is  12 V

Answer:

The value  is  [tex]N_s  =  21 \  turns [/tex]

Explanation:

From the equation we are told that

   The input voltage is  [tex]V_{in}  = 120 \ V[/tex]

   The number of turns of the primary coil is [tex]N_p =  210 \  turn[/tex]

    The output from the secondary is [tex]V_o =  12V[/tex]

From the transformer equation

   [tex]\frac{N_p}{V_{in}}  =\frac{N_s}{V_o}[/tex]

Here [tex]N_s[/tex] is the number of turns in the secondary coil

=> [tex]N_s  =  \frac{N_p}{V_{in}}  *  V_s[/tex]

=>[tex]N_s  =  \frac{210}{120}  *  12[/tex]

=>[tex]N_s  =  21 \  turns [/tex]

Answer:

Dividing the silicon density by 1000 and then multiply it by 1000000.

Explanation:

A kilogram equals 1000 grams and a cubic meter equals 1000000 cubic centimeters. Hence, we must divide the silicon density by 1000 and then multiply itby 1000000 to convert the value into kilograms per cubic centimeter. That is:

[tex]x = 2.33\,\frac{g}{cm^{3}}\times \frac{1\,kg}{1000\,g}\times \frac{1000000\,cm^{3}}{1\,m^{3}}[/tex]

[tex]x = 2330\,\frac{kg}{m^{3}}[/tex]

In a nutshell, we must multiply the density of silicon by 1000 to obtains its value in kilograms per cubic meter.

Answer:

The net force on an object is the total force applied on the object after adding  up all the forces

In the given diagram,

we can see that the 2 forces of 4N and 4N will cancel each other out since they are equal and in the opposite direction

Now, we are left with a force of 2N and 10N,

the net force will be the difference of these forces:

Net force = 10N - 2N

Net force = 8N downwards

Another way to do it:

The two 4N forces will be cancelled out,

and we are left with a 2N and a 10N force

(notice how we cancelled equal and opposite forces for the 4N)

We can divide the 10N force into (2N + 8N)

Since the 2N forces are equal and opposite, they will be cancelled out

and we will be left with a net force of 8N downwards

Answer:

Explanation:

Let the velocity be v .

vertical component of the velocity = v sin 60 = √3 v /2

it reaches maximum height of 10 m .

v² = 2 gh

( √3 v/2 )² = 2 x 9.8 x 10

3 v² = 196 x 4

v² = 65.33 x 4

v = 16.2  m /s

Let time taken to reach height of 10 m

v = u - gt

v sin 60 = 9.8 t

16.2 x √3  /2 = 9.8 t

t = 1.43 s

horizontal distance covered = v cos 60 x t

16.2 x .5 x 1.43 = 11 .5 m

Answer:

(a) 102 cm/s

(b) 0.490 cm²

Explanation:

(a) Use Bernoulli equation.

P₁ + ½ ρ v₁² + ρgh₁ = P₂ + ½ ρ v₂² + ρgh₂

0 + ½ ρ v₁² + ρgh₁ = 0 + ½ ρ v₂² + 0

½ ρ v₁² + ρgh₁ = ½ ρ v₂²

½ v₁² + gh₁ = ½ v₂²

½ (25.0 cm/s)² + (980 cm/s²) (5.00 cm) = ½ v²

v = 102 cm/s

(b) The flow rate is constant.

v₁ A₁ = v₂ A₂

(25.0 cm/s) (2.00 cm²) = (102 cm/s) A

A = 0.490 cm²

Answer:

1. [tex] E = 1.14 \cdot 10^{13} N/C [/tex]

2. [tex]E_{k} = 9.1 \cdot 10^{-17} J[/tex]      

Explanation:

1. The strength of the nucleus' electric field (E):

[tex]E = \frac{kq}{r^{2}}[/tex]

Where:

k: is the Coulomb constant = 9x10⁹ Nm²/C²

q: is the proton charge = 1.6x10⁻¹⁹ C

r: is the radius = 10⁻¹⁰ m

[tex]E = \frac{kq}{r^{2}} = \frac{9\cdot 10^{9} Nm^{2}/C^{2}*79*1.6 \cdot 10^{-19} C}{(10^{-10} m)^{2}} = 1.14 \cdot 10^{13} N/C[/tex]

2. The kinetic energy (Ek) of an electron is the following:

[tex] E_{k} = \frac{1}{2}mv^{2} [/tex]    

Where:

m is the electron's mass = 9.1x10⁻³¹ kg

v: is the speed of the electron

We can find the speed of the electron by equaling the centripetal force (Fc) and the electrostatic force (Fe):

[tex] F_{c} = F_{e} [/tex]  

[tex] \frac{mv^{2}}{r} = \frac{kq^{2}}{r^{2}} = qE [/tex]

[tex] v^{2} = \frac{qEr}{m} = \frac{1.6 \cdot 10^{-19} C*1.14 \cdot 10^{13} N/C*10^{-10} m}{9.1 \cdot 10^{-31} kg} = 2.00 \cdot 10^{14} m^{2}/s^{2} [/tex]                  

Now, we can find the kinetic energy:

[tex] E_{k} = \frac{1}{2}mv^{2} = \frac{1}{2}9.1 \cdot 10^{-31} kg*2.00 \cdot 10^{14} m^{2}/s^{2} = 9.1 \cdot 10^{-17} J [/tex]    

I hope it helps you!

Answer:

Explanation:

mass of water coming out per second = A x v where A is area of cross section of the nozzle and v is velocity of water

A = 3.14 x .005²

= 785 x 10⁻⁷ m²

mass of water coming out per second = 785 x 10⁻⁷ x 30 = 23.55 x 10⁻⁴ kg

momentum of this mass = 23.55 x 10⁻⁴ x 30 = 706.5 x 10⁻⁴ kg m /s .

Rate of change of momentum  = 706.5 x 10⁻⁴

Let force be F

F - mg = 706.5 x 10⁻⁴

F = mg + 706.5 x 10⁻⁴

F =  23.55 x 10⁻⁴  x 9.8 + 706.5 x 10⁻⁴

= 937.3 x 10⁻⁴ N .

Answer:

I believe the electromagnetic field should be reversed.

Explanation:

When a student creates an electromagnetic wave and then reverses the direction of the current, the direction of the magnetic field will be reversed.

An electromagnetic wave may be defined as a type of wave that is significantly created as a result of vibrations between an electric field and a magnetic field. These waves are composed of oscillating magnetic and electric fields.

According to the context of this question, when an individual is constructing an electromagnetic wave and then reverses the direction of the current, it will eventually affect the direction of the magnetic field in the same direction with respect to the current. So, if the direction of the current is reversed, the direction of the magnetic field would also be reversed.

Therefore, when a student creates an electromagnetic wave and then reverses the direction of the current, the direction of the magnetic field will be reversed.

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Your question seems incomplete. The most probable complete question is as follows:

A student creates an electromagnetic wave and then reverses the direction of the current. Which of the following will happen to the magnetic field?

Answer:

(a) 22 kN

(b) 36 kN, 29 kN

(c) left will decrease, right will increase

(d) 43 kN

Explanation:

(a) When the truck is off the bridge, there are 3 forces on the bridge.

Reaction force F₁ pushing up at the first support,

reaction force F₂ pushing up at the second support,

and weight force Mg pulling down at the middle of the bridge.

Sum the torques about the second support.  (Remember that the magnitude of torque is force times the perpendicular distance.  Take counterclockwise to be positive.)

∑τ = Iα

(Mg) (0.3 L) − F₁ (0.6 L) = 0

F₁ (0.6 L) = (Mg) (0.3 L)

F₁ = ½ Mg

F₁ = ½ (44.0 kN)

F₁ = 22.0 kN

(b) This time, we have the added force of the truck's weight.

Using the same logic as part (a), we sum the torques about the second support:

∑τ = Iα

(Mg) (0.3 L) + (mg) (0.4 L) − F₁ (0.6 L) = 0

F₁ (0.6 L) = (Mg) (0.3 L) + (mg) (0.4 L)

F₁ = ½ Mg + ⅔ mg

F₁ = ½ (44.0 kN) + ⅔ (21.0 kN)

F₁ = 36.0 kN

Now sum the torques about the first support:

∑τ = Iα

-(Mg) (0.3 L) − (mg) (0.2 L) + F₂ (0.6 L) = 0

F₂ (0.6 L) = (Mg) (0.3 L) + (mg) (0.2 L)

F₂ = ½ Mg + ⅓ mg

F₂ = ½ (44.0 kN) + ⅓ (21.0 kN)

F₂ = 29.0 kN

Alternatively, sum the forces in the y direction.

∑F = ma

F₁ + F₂ − Mg − mg = 0

F₂ = Mg + mg − F₁

F₂ = 44.0 kN + 21.0 kN − 36.0 kN

F₂ = 29.0 kN

(c) If we say x is the distance between the truck and the first support, then using our equations from part (b):

F₁ (0.6 L) = (Mg) (0.3 L) + (mg) (0.6 L − x)

F₂ (0.6 L) = (Mg) (0.3 L) + (mg) (x)

As x increases, F₁ decreases and F₂ increases.

(d) Using our equation from part (c), when x = 0.6 L, F₂ is:

F₂ (0.6 L) = (Mg) (0.3 L) + (mg) (0.6 L)

F₂ = ½ Mg + mg

F₂ = ½ (44.0 kN) + 21.0 kN

F₂ = 43.0 kN

Answer:

Explanation:

given:

weight of bridge = 44 kN

weight of truck = 21 kN

a) truck is off the bridge

since the bridge is symmetrical, left support is equal to right support.

Left support = Right support = 44/2

Left support = Right support = 22 kN

b) truck is positioned  as shown.

to get the reaction at left support, take moment from right support = 0

∑M at Right support = 0

Left support (0.6) - weight of bridge (0.3) - weight of truck (0.4) = 0

Left support = 44 (0.3) + 21 (0.4)  

                                  0.6

Left support = 36 kN

Right support = weight of bridge + weight of truck - Left support

Right support = 44 + 21 - 36

Right support = 29 kN

c)

as the truck continues to drive to the right, Left support will decrease

as the truck get closer to the right support,  Right support will increase.

d) truck is directly under the right support, find reaction at Right support?

∑M at Left support = 0

Right support (0.6) - weight of bridge (0.3) - weight of truck (0.6) = 0

Right support = 44 (0.3) + 21 (0.6)  

                                  0.6

Right support = 43 kN

Answer:

The period of that same pendulum on the moon is 12.0 seconds.

Explanation:

To determine the period of that same pendulum on the moon,

First, we will determine the value of g (which is a measure of the strength of Earth's gravity) on the Moon. Let the value of g on the Moon be [tex]g_{M}[/tex].

From the question, the strength of earth’s gravity is only 1/6th of the normal value. The normal value of g is 9.8 m/s²

∴ [tex]g_{M}[/tex] = [tex]\frac{1}{6} \times 9.8 m/s^{2}[/tex]

[tex]g_{M}[/tex] = 1.63 m/s²

From the question, T=2π√L/g

[tex]T = 2\pi \sqrt{\frac{L}{g} }[/tex]

We can write that,

[tex]T_{E} = 2\pi \sqrt{\frac{L}{g_{E} } }[/tex] .......... (1)

Where [tex]T_{E}[/tex] is the period of the pendulum on Earth and [tex]g_{E}[/tex] is the measure of the strength of Earth's gravity

and

[tex]T_{M} = 2\pi \sqrt{\frac{L}{g_{M} } }[/tex] .......... (2)

Where [tex]T_{M}[/tex] is the period of the pendulum on Moon and [tex]g_{M}[/tex] is the measure of the strength of Earth's gravity on the Moon.

Since we are to determine the period of the same pendulum on the moon, then, [tex]2\pi[/tex] and [tex]L[/tex] are constants.

Dividing equation (1) by (2), we get

[tex]\frac{T_{E} }{T_{M} } = \sqrt{\frac{g_{M} }{g_{E} } }[/tex]

From the question,

[tex]T_{E} = 4.9secs[/tex]

[tex]g_{E}[/tex] = 9.8 m/s²

[tex]g_{M}[/tex] = 1.63 m/s²

[tex]T_{M}[/tex] = ??

From,

[tex]\frac{T_{E} }{T_{M} } = \sqrt{\frac{g_{M} }{g_{E} } }[/tex]

[tex]\frac{4.9}{T_{M} } = \sqrt{\frac{1.63}{9.8} }[/tex]

[tex]\frac{4.9}{T_{M} } = 0.40783[/tex]

[tex]T_{M} =\frac{4.9}{0.40783 }[/tex]

[tex]T_{M} = 12.01 secs[/tex]

∴ [tex]T_{M} = 12.0secs[/tex]

Hence, the period of that same pendulum on the moon is 12.0 seconds.

Answer:

The period of that same pendulum on the moon is 12.0 s

Explanation:

Given;

period of a pendulum’s swinging, T=2π√L/g

the strength of earth’s gravity on moon, g₂ = ¹/₆(g₁)

period of pendulum on Earth, T₁ = 4.9 s

period of pendulum on moon, T₂ = ?

The length of the pendulum is constant, make it the subject of the formula;

[tex]T = 2\pi \sqrt{\frac{L}{g} }\\\\\frac{T}{2\pi} = \sqrt{\frac{L}{g}}\\\\(\frac{T}{2\pi} )^2 =\frac{L}{g}\\\\\frac{T^2}{4\pi^2} = \frac{L}{g}\\\\ L = \frac{gT^2}{4\pi^2}\\\\L_1 = L_2\\\\\frac{g_1T_1^2}{4\pi^2}= \frac{g_2T_2^2}{4\pi^2}\\\\g_1T_1^2 = g_2T_2^2\\\\T_2^2 = \frac{g_1T_1^2}{g_2} \\\\T_2 = \sqrt{\frac{g_1T_1^2}{g_2}}\\\\ T_2 = \sqrt{\frac{g_1T_1^2}{g_1/6}}\\\\ T_2 = \sqrt{\frac{6*g_1T_1^2}{g_1}}\\\\T_2 = \sqrt{6T_1^2}\\\\ T_2 = T_1\sqrt{6} \\\\T_2 = (4.9)\sqrt{6}\\\\ T_2 = 12.0 \ s[/tex]

Therefore, the period of that same pendulum on the moon is 12.0 s

Answer:

We are given:

V1 = 5.5L          T1 = -38 C   or   235 k

V2 = 1.3L           T2 = T

From the gas equation:

PV = nRT

Since the pressure (P) , number of moles (n) and the universal gas constant (R) are constants, we can write the same equation as:

V / T = k  (where k is a constant)

so a bit more insight, since the values noted above are constant, when multiplied by each other, they will provide us with a constant number irrespective of the value of the variables

Changing the variables for the first case:

V1 / T1 = k   (where k is the same constant) ----------------(1)

Similarly,

V2 / T2 = k  (again, k has the same value)----------------(2)

From (1) and (2):

k is the common value

V1 / T1 = V2 / T2

Replacing the variables

5.5 / 235 = 1.3 / T

T = 1.3 * 235 / 5.5

T = 55.54 k

Therefore, at 55.54 K the gas will have a volume of 1.3L

Answer:

(a) [tex]2\vec A=12\hat i-4\hat j+6\hat k[/tex]

(b) [tex]\displaystyle \vec{U_A}=12/7\hat i-4/7\hat j+6/7\hat k[/tex]

(c) [tex]-4\vec{U_A}=-48/7\hat i+16/7\hat j-24/7\hat k[/tex]

Explanation:

Vectors

Given a vector

[tex]\vec A=6\hat i-2\hat j+3\hat k[/tex]

We must determine the following:

a) A vector in the same direction as A with double magnitude 2A.

If the vector goes in the same direction but has a different magnitude, we only need to multiply each component by a common factor, in this case, by 2. Thus, the required vector is:

[tex]2\vec A=12\hat i-4\hat j+6\hat k[/tex]

b) A unit vector in the same direction of A.

The unit vector needs to compute the magnitude of the vector:

[tex]\mid A\mid=\sqrt{6^2+2^2+3^2}[/tex]

[tex]\mid A\mid=\sqrt{36+4+9}=\sqrt{49}=7[/tex]

[tex]\mid A\mid=7[/tex]

The unit vector is:

[tex]\displaystyle \vec{U_A}=\frac{\vec A}{\mid \vec A\mid}[/tex]

[tex]\displaystyle \vec{U_A}=\frac{12\hat i-4\hat j+6\hat k}{7}[/tex]

[tex]\displaystyle \vec{U_A}=12/7\hat i-4/7\hat j+6/7\hat k[/tex]

c) A vector opposite to A with magnitude 4 m. We assume the original vector is also expressed in m.

The opposite vector to A is obtained simply by multiplying the unit vector by -1. To make its magnitude equal to 4, also multiply by 4. In all, we multiply the unit vector by -4:

[tex]-4\vec{U_A}=-4(12/7\hat i-4/7\hat j+6/7\hat k)[/tex]

[tex]-4\vec{U_A}=-48/7\hat i+16/7\hat j-24/7\hat k[/tex]