Jennifer has taught her pet rat to run a maze. She thinks that the rat will
go faster if she puts its favorite treat at the end. She has the rat run the
maze ten times with the favorite treat and ten times with a regular food
pellet. She uses a stopwatch to measure how long it takes for the rat to get
to the reward.
O Replication
O Repetition

Answer:

 #_bills = 2.59 10⁸  Bills

Explanation:

For this exercise we must calculate the length of the Earth's circle

        L = 2π r

Let's reduce to the SI system

        r = 6.40 10³ km (1000m / 1km) = 6.40 10⁶ m

        d = 15.5 cm (1m / 100cm) = 0.155 m

        L = 2π 6.40 10⁶

        L = 40.21 10⁶ m

now we can use a direct rule of proportions (rule of three). If 1 bill has d = 0.155, how much bill will have L

       #_bills = 1 L / d

       #_bills = 1 40.21 10⁶6 / 0.155

       #_bills = 2.59 10⁸  Bills

the total number of bills is  2.6 10⁸ bills

Answer:

(a) 4.83 seconds

(b) 167.3m

(c) 40m

Explanation:

This is a two-dimensional motion. Therefore, the components of the initial velocity - [tex]u_X[/tex] and [tex]u_Y[/tex] - in the x and y directions are given as follows:

[tex]u_X[/tex] = u cos θ                 --------------(*)

[tex]u_Y[/tex] = u sin θ                -------------(**)

Where

θ = angle of projection

(a) To calculate the time taken for the apple to strike the ground.

For simplicity, let's first calculate the maximum height H reached by the apple.

Using one of the equations of motion as follows, we can find H:

v² = u² + 2as               ---------------(i)

Where;

v = velocity at maximum height = 0 [at maximum height, velocity is 0]

u = initial vertical velocity of the apple = [tex]u_Y[/tex]

=> u = [tex]u_Y[/tex] = u sin θ

=> [tex]u_Y[/tex] = 40 sin 30°

=> [tex]u_Y[/tex] = 40 x 0.5

=> [tex]u_Y[/tex] = 20 m/s

a = acceleration due to gravity = -g [apple moves upwards against gravity]

a = -10m/s²

s = H = maximum height reached from the top of the building

Substitute these values into equation (i) above to have;

0² = [tex]u_Y[/tex]² + 2aH

0² = (20)² + 2(-10)H

0 = 400 - 20H

20H = 400

H = 20m

The total time taken to strike the ground is the sum of the time taken to reach maximum height and the time taken to strike the ground from maximum height.

=>Calculate time t₁ to reach maximum height.

Using one of the equations of motion, we can calculate t₁ as follows;

v = [tex]u_Y[/tex]  + at                ---------------(ii)

Where;

v = velocity at maximum height = 0

u = initial vertical velocity of the apple = [tex]u_Y[/tex]

a = -g = -10m/s²           [acceleration due to gravity is negative since the apple is thrown upwards to reach maximum height]

t = t₁ = time taken to reach maximum height.

Equation (ii) then becomes;

0 = 20  + (-10)t₁

10t₁ = 20

t₁ = 2 seconds

=>Calculate time t₂ to strike the ground from maximum height.

Now, using one of the equations of motion, we can calculate the time taken as follows;

Δy = [tex]u_Y[/tex] t + [tex]\frac{1}{2}[/tex]at                ---------------(iii)

Where;

Δy = displacement from maximum height to the ground = maximum height from top of building + height of building = 20 + 20 = 40m

a = g = 10m/s²            [acceleration due to gravity is positive since the apple is now coming downwards from maximum height]

t = t₂    [time taken to strike the ground from maximum height]

[tex]u_Y[/tex] = initial vertical velocity from maximum height = 0

[tex]u_Y[/tex] = 0

Equation (iii) then becomes

40 = 0t + [tex]\frac{1}{2}[/tex](10)t₂²

40 = 5t₂²            [divide through by 5]

8 = t₂²

t₂ = ±[tex]\sqrt{8}[/tex]

t₂ = ±[tex]2\sqrt{2}[/tex]

t₂ = +2[tex]\sqrt{2}[/tex] or -2[tex]\sqrt{2}[/tex]

since time cannot be negative,

t₂ = 2[tex]\sqrt{2}[/tex] = 2.83 seconds

Therefore, the time taken for the apple to strike the ground is;

t₁ + t₂ = 2 +  2.83 = 4.83 seconds

(b) The distance from the foot of the building where the apple will strike the ground

Since this is the horizontal distance, we use the horizontal version of equation (iii) as follows;

Δx = [tex]u_X[/tex] t + [tex]\frac{1}{2}[/tex]at       -----------(v)

Where

Δx = distance from the foot of the building to where the apple strikes the ground.

[tex]u_X[/tex] = initial horizontal velocity of the apple as expressed in equation (*)

[tex]u_X[/tex] = 40 cos 30

[tex]u_X[/tex] = 34.64 m/s

t = time taken for the motion of the apple = 4.83 seconds [calculated above]

a = acceleration due to gravity in the horizontal direction = 0. [For a projectile, there is no acceleration in the horizontal direction since velocity is constant]

Substitute these values into equation (v) as follows;

Δx = [tex]u_X[/tex] t + [tex]\frac{1}{2}[/tex](0)t

Δx = 34.64 x 4.83

Δx = 167.3 m

Therefore, the distance from the foot of the building is 167.3m

(c) The maximum height reached by the apple from the ground

This is the sum of the height reached from the top of the building (20m which has been calculated in (a) above) and the height of the building.

= 20m + 20m = 40m

Answer:

The minimum thickness of the soap bubble for destructive interference to occur is 225.56 nm.

Explanation:

Given;

wavelength of light, λ = 600 nm

The minimum thickness of the soap bubble for destructive interference to occur is given by;

[tex]t = \frac{\lambda/n}{2}\\\\t = \frac{\lambda}{2n}[/tex]

where;

n is refractive index of soap film = 1.33

[tex]t = \frac{\lambda}{2n} \\\\t = \frac{600*10^{-9}}{2(1.33)}\\\\t = 2.2556 *10^{-7} \ m\\\\t = 225.56 *10^{-9} \ m\\\\t = 225.56 \ nm[/tex]

Therefore, the minimum thickness of the soap bubble for destructive interference to occur is 225.56 nm.

Answer:

the answer should be gasses

Answer:

Explanation:

The earth-atmosphere energy balance is the balance between incoming energy from the Sun and outgoing energy from the Earth. Energy released from the Sun is emitted as shortwave light and ultraviolet energy. When it reaches the Earth, some is reflected back to space by clouds, some is absorbed by the atmosphere, and some is absorbed at the Earth's surface.

Hope this helped you!

Answer:

[tex] \boxed{ \bold{ \sf{see \: below}}}[/tex]

Explanation:

[tex] \boxed{ \bold{ \underline{ \huge{ \boxed{ \sf{ohm's \: law}}}}}}[/tex]

The relation between current through a metallic conductor and potential difference across its ends was studied systematically by a German physicist , George Simon Ohm in 1826 AD . This relation is now known as Ohm's law. It states that the electric current passing through a conductor is directly proportional to the potential difference across its two ends at a constant physical condition [ Temperature , cross - sectional area , length , nature of material etc ]

Hope I helped!

Best regards!!

Answer:

840 cm

Explanation:

Note: A hydraulic press operate based on pascal's principle.

From pascal's principle

W₁/d₁ = W₂/d₂...................... Equation 1

Where W₁ and W₂ are the first and second weight, and d₁ and d₂ are the  first and second diameter of the piston.

make d₁ the subject of the equation

d₁ = W₁×d₂/W₂................ Equation 2

Given: W₁ = 2100 kg, W₂ = 25 kg, d₂ = 10 cm = 0.1 m.

Substitute these values into equation 2

d₁ = 2100(0.1)/25

d₁ = 8.4 m

d₁ = 840 cm

Answer:

14.57 ohms

Explanation:

Here in the figure ,Rb & R₄are in series  & also  Rc & R₅ are in series. As they are in series , ( Rb + R₄ ) & (Rc & R₅) are in parallel . So the equivalent resistance in that branch = ( 2 + 18 ) ║ ( 3 + 12 )

                                          = 20 ║ 15

                                          = (20×15) / (20 + 15)

                                          = 8.57 ohms

Also Ra ( 6 ohm ) is in series with that branch ,. So the equivalent resistance of the whole circuit = 8.57 + 6 = 14.57 ohms.

total resistance is 26 ohm and voltage across [tex]R_C[/tex] resister is 1.1554 Ampere.

According to the circuit,

[tex]R_A[/tex] = 6 Ω.

[tex]R_B[/tex] = 2 Ω.

[tex]R_C[/tex] = 3 Ω.

R₄ = 18 Ω.

R₅ = 12 Ω.

V = 10 V.

In the circuit, the series combination of [tex]R_C[/tex] and R₅ is parallel connected with series combination of [tex]R_B[/tex] and R₄. And this network is connected with [tex]R_A[/tex] in series combination.

So, Equivalent resistance of the circuit is; R =  [tex]R_A[/tex] + ( [tex]R_C[/tex] + R₅) II ([tex]R_B[/tex] +R₄)

=   18 Ω + ( 3 Ω +  12 Ω)II(2 Ω+ 18 Ω)

=  18 Ω + 15ΩII20Ω

=   18 Ω  + (15×20)/(15+20)Ω

= 18 Ω + 8.57 Ω

= 26 Ω

So, current flowing through the circuit: I = V/ R = 10V / 26Ω = 0.38 Amp.

Voltage drop across the parallel network; V₁ =  V - I[tex]R_A[/tex]

= 10V - 0.38×6 V

= 7.72 V.

So, voltage across the resister [tex]R_C[/tex] = V₁[tex]R_C[/tex]/[tex](R_C[/tex] + R₅)

= 7.72 × 3/(3 + 12) Amp

= 1.1544 Amp.

Hence, total resistance is 26 ohm and voltage across specific resister is 1.1554 Ampere.

Learn more about circuit here:

https://brainly.com/question/21505732

#SPJ3

Answer: please find the answer in the explanation.

Explanation:

Harmonic can be experienced by any body that repeats itself. The pattern can be sinusoidal, square, tooth etc.

The fundamental differences between the harmonic oscillator dynamics and the simple pendulum dynamics are:

1.) The harmonic oscillator dynamics can be sinusoidal or square wave so far the motion is periodic while the simple pendulum dynamics is always sinusoidal.

2.) In simple pendulum dynamics, the period of oscillation is independent of the amplitude. While the period in harmonic oscillator dynamics depends on the amplitude.

3.) Differential equation is only one method to analyze the simple pendulum dynamics where there are several methods to analyze the harmonic oscillator dynamics.

Answer:

Tension in each cable = 175 N

Explanation:

Given:

Number of cables = 2

Weight of sign board(T) = 350 N

Find:

Tension in each cable

Computation:

We know that,

T1 = T2

So,

T1 + T2 = T

T1 + T2 = 350

T1 + T1 = 350

T1 = 175

Tension in each cable = 175 N

Answer:

Reactance of the capacitor is 0.01 ohms.

Explanation:

It is given that,

Capacitance of the capacitor is 0.5 F

Peak voltage of the battery is 2 V

Angular frequency is 200 rad/s

We need to find the capacitive reactance. The capacitive reactance is due to the capacitor in the circuit. It is given by :

[tex]X_c=\dfrac{1}{\omega C}\\\\X_c=\dfrac{1}{200\times 0.5}\\\\X_c=0.01\ \Omega[/tex]

So, the reactance is 0.01 ohms.

Answer:

C

Explanation:

                                                    = (5000 kg)·(100 m/s)

                                                    = 500,000 kg·m/s.

                          5000+M) kg)·(50 m/s) = 500,000 kg·m/s

         Dividing by 50 m/s and subtracting 5000 kg, we have ...

                                          (5000 +M) kg = 10,000 kg

                                                        M kg = 5000 kg

Answer:

Because the force F is always at 90 degrees to the velocity of the particle.

Explanation:

The factors that determine the path of a particle in a uniform magnetic field depend on

The magnetic flux density

The charge on the particle

The speed of the particle

Why is the trajectory of the positively charged particle curving down, to the bottom of the screen, when moving in the magnetic field?

Because the force F is always at 90 degrees to the velocity of the particle.

This can be illustrated by the equation

F = BQVSINØ

The magnetic force is always acting perpendicular to the particle velocity and its direction can be found using the left hand rule.

Answer:

The  value is   [tex]V_d  = 5 \ V[/tex]

Explanation:

From the question we are told that

    The  capacitance of the capacitor is [tex]C =  0.16 \  pF  =  0.16*10^{-12} \ F[/tex]

     The  voltage is  [tex]V  =  10\ V[/tex]

    The number of electrons present on the negative plate is  [tex]N_e  =  1.00 *10^{7} \  electrons[/tex]

     Generally the charge on the positive plate at 10 Volt is mathematically represented as

            [tex]Q_a =  C *  V[/tex]

     =>   [tex]Q_a  =  0.16*10^{-12} *  10[/tex]

     =>    [tex]Q_a  =  0.16*10^{-11} \  C[/tex]

Now the charge  on the plate when the electron where placed is evaluated as

    [tex]Q_b  =  Q_a  + ( N_e * e)[/tex]

Where e  is the charge on each electron with a value  [tex]e =  1.60 *10^{-19} \ C[/tex]

     =>    [tex]Q_b  =  0.16*10^{-11} + (1.0*10^7 *  1.60*10^{-19})[/tex]

      =>  [tex]Q_b  = 3.2 *10^{-12 } \  C[/tex]

Generally the voltage between the two plate is evaluated as

       [tex]V_d  =  \frac{ Q_b  -  Q_a  }{ 2 * C }[/tex]

=>     [tex]V_d  = \frac{ 3.2*10^{-12} -  0.16*10^{-11}}{2 *  0.16 *10^{-12}}[/tex]

=>      [tex]V_d  = 5 \ V[/tex]

Answer:

magnitude = 3

unit vector = [tex]\frac{2i}{3} - \frac{j}{3} - \frac{2k}{3}[/tex]

Explanation:

Given vectors:

u = 2i + 2j - k

v = -i + k = -i + 0j + k

(a) u x v is the cross product of u and v, and is given by;

[tex]u X v = \left[\begin{array}{ccc}i&j&k\\2&2&-1\\-1&0&1\end{array}\right][/tex]

u x v = i(2+0) - j(2 - 1) + k(0 - 2)

u x v = 2i - j - 2k

Now the magnitude of u x v is calculated as follows:

| u x v | = [tex]\sqrt{2^2 + (-1)^2 + (-2)^2}[/tex]

| u x v | = [tex]\sqrt{4 + 1 + 4}[/tex]

| u x v | = [tex]\sqrt{9}[/tex]

| u x v | = 3

Therefore, the magnitude of u x v is 3

(b) The unit vector û parallel to u x v in the direction of u x v is given by the ratio of u x v and the magnitude of u x v. i.e

û = [tex]\frac{u X v}{|u X v|}[/tex]        

u x v = 2i - j - 2k        [calculated in (a) above]

|u x v| = 3                   [calculated in (a) above]

∴ û = [tex]\frac{2i - j - 2k}{3}[/tex]

∴ û = [tex]\frac{2i}{3} - \frac{j}{3} - \frac{2k}{3}[/tex]

Answer:

(-2.57*10^20, 3.67*10^20, 0)

Explanation:

Refer to the attachment.

I hope that helps

Answer:

Lead is melted into a liquid to form pellets.

Answer:

C. lead is melted into a liquid to form pellets

Explanation:

Answer:

Explanation:

Let the intensity  of unpolarised light be I₀ . After passing through the first polarising filter , the intensity  is I₀ / 2 .

After second filter , the intensity  will be  I₀ / 2 x cos²45 =  I₀ / 4

After third filter , the intensity will be I₀ / 4  x cos²45 = I₀ / 8 .

So,

1 / 8 the of initial light passes through the last filter .

Answer:

Centripetal Force = 483.3 N

Explanation:

A centripetal force is the force that tends to keep a mocing object along a curved path and it is directed towards the centre of the rotatio, while centrifugal force is an apparent force that tends to force a rotating object away from the center of the rotation.

The formula for centripetal force is given by:

[tex]F_c = \frac{mv^2}{r} \\where:\\F_C = centripetal\ force\\m = mass\ = 22kg\\\omega =angular\ velocity = 40.0\ rev/min[/tex]

Let us work on the angular velocity (ω), by converting to radians/ seconds

ω = 40 rev/min,

1 rev = 2π rad

∴ 40 rev = 2π × 40 rad = 80π rad

1 min = 60 seconds

[tex]\therefore\ 40\ rev \slash min = \frac{80\ \times\ \pi\ rad}{60\ seconds} \\40\ rev \slash min = 4.189\ rad \slash sec[/tex]

Next let us find the velocity (v) from the angular velocity. Velocity (v) and angulsr velocity (ω) are related by the equation:

v = ω × r (m/s)

v = 4.189 × 1.25

v = 5.24 m/s

Finally, the centripetal force is calculated thus:

[tex]F_c = \frac{mv^2}{r} \\\\F_c = \frac{22 \times (5.24)^2 }{1.25} \\\\F_c = \frac{604.07}{1.25}\\ F_c = 483.3N[/tex]

Answer:

Sound waves reaching the olfactory mucosa do not elicit olfactory perception due to the ___MODALITY_________ not matching the type of stimulus of the receptos

Explanation:

Because modality of sensation refers to what is perceived after the stimulus is effected eg the pressure modality is effected when the pressure receptors of the skin are stimulated so in this case sound will not elite olfactory sensation because the modality here is sound rather than smell

Answer:

Yes, there is such a way.

Explanation:

If currents flow in the same direction in two or more long parallel wires, there will be an attractive force between the wires. If the current flows in different directions, there will be a repulsive force between the wires. In this case, these three parallel wires, can be be made to carry current in the same direction, creating an attractive force between all three wires.

Note that it is not possible to have at the least one of them carry current in the opposite direction and still have an attractive current between them.

Answer:

The value is  [tex]\Delta h = 0.003 \ m[/tex]

Explanation:

From the question we are told that

   The  height of the water is  [tex]h_1 = 10 \ cm = 0.10 \ m[/tex]

    The  density of  oil is [tex]\rho_o = 950 \ kg/m^3[/tex]

  The  height of  oil  is  [tex]h_2 = 6 \ cm = 0.06 \ m[/tex]

Given that both arms of the tube are open then the pressure on both side is the same

So  

      [tex]P_a = P_b[/tex]

=>   Here  

             [tex]P_a = P_z + \rho_w * g * h[/tex]

where  [tex]\rho_w[/tex] is the density of water with value  [tex]\rho_w = 1000 \ kg/m^3[/tex]

and  [tex]P_z[/tex] is the atmospheric pressure

and  

        [tex]P_b = P_z + \rho_o * g * h_2[/tex]

=>   [tex]P_z + \rho_w * g * h = P_z + \rho_o * g * h_2[/tex]

=>    [tex]\rho_w * h = \rho_o * h_2[/tex]

=>      [tex]h = \frac{950 * 0.06 }{1000}[/tex]

=>      [tex]h = 0.057 \ m[/tex]

The  difference in height is evaluated as    

           [tex]\Delta h = 0.06 - 0.057[/tex]

          [tex]\Delta h = 0.003 \ m[/tex]

1.) equal volume of different substances have "different" masses.

2.)The more closely packed arrangement the particles of a substance have, "increases" its density.

3.)the SI unit of power is "Watts".

4.)an iron nail sinks in water but floats on " mercury ".

5.)balloons used for advertisements are filled with " helium" gas.

6.)"Conduction" is the primary mode of heat transfer in liquid and gases.

I hope this helps you...

Answer:

The speed is 401.76m/s

Explanation:

To find the fundamental frequency we use

3rd.harmonic - 2nd.harmonic = 324Hz

And we know that

f=v/2L

So v=f2L

v= 324 x 2 x 0.62= 401.76m/s

Answer:

The average speed is 3.5 mi/h

Explanation:

Average speed is given by

[tex]Average speed = \frac{Total distance}{Total time}[/tex]

If the total distance covered is [tex]x[/tex] mi,

Then [tex]\frac{2}{3}x[/tex] mi was covered while hiking and

[tex]\frac{1}{3}x[/tex] mi was covered while running.

Now, we will find the time taken while hiking and the time taken while running

[tex]Speed = \frac{Distance}{ Time}\\ Time = \frac{Distance}{Speed}[/tex]

Speed = 2.9 mi/h

Distance = [tex]\frac{2}{3}x[/tex] mi

From,

[tex]Time = \frac{Distance}{Speed}[/tex]

[tex]Time = \frac{\frac{2}{3}x }{2.9}[/tex]

Time = [tex]0.2299x[/tex] h

Time taken while hiking is 0.2299 h

Speed = 5.6 mi/h

Distance = [tex]\frac{1}{3}x[/tex] mi

[tex]Time = \frac{Distance}{Speed}[/tex]

[tex]Time = \frac{\frac{1}{3}x }{5.6}[/tex]

Time = [tex]0.05952x[/tex] h

Now, for the average speed

[tex]Average speed = \frac{Total distance}{Total time}[/tex]

Total distance = [tex]\frac{2}{3}x[/tex] mi  + [tex]\frac{1}{3}x[/tex] mi = [tex]x[/tex] mi

Total time = [tex]0.2299x[/tex] + [tex]0.05952x[/tex] = [tex]0.28942x[/tex] h

∴ [tex]Average speed = \frac{x}{0.28942x}[/tex]

Average speed = 3.4552 mi/h

Average speed ≅ 3.5 mi/h

Answer:

hello the diagram related to your question is missing attached below is the missing diagram

answer : 107.07⁰

Explanation:

The direction of the force can be calculated as below

angle = 180 - ∝ - ∅  ------ 1

∅ = [tex]tan^{-1} b/a[/tex] = tan^-1 ( 0.429 )

∅ = 23.2⁰

∝  can be determined by applying the parallelogram law

∝ = [tex]tan^{-1} ( \frac{R24sin56.4}{f13 + R24cos56.4} )[/tex]

   = tan^-1 ( 21.173 / 17.935 )

∝ = 49.73⁰    

back to equation 1 direction of force with positive angle

= 180 - 49.73 - 23.2 = 107.07⁰

Answer:

Uninvolved parenting style

Explanation:

Uninvolved parenting style is the parenting style which is thought to produce children who grow up to be emotionally withdrawn, distant, and lacking in curiosity.

This is usually because there is little or no contact between the parents and children which leaves a wide gap and the children start to become emotionally withdrawn as a result. They also aren’t curious to learn new things as a result of the absence of parental care.

Answer:

1222.45 Kg/m³

Explanation:

The following data were obtained from the question:

Dimension of rectangular block = 22 cm x 13.2 cm x 4.4 cm

Mass (m) = 1562.0 g

Density (D) =?

Next, we shall determine the volume of the rectangular block.

This is illustrated below:

Volume = length x breadth x height

V = 22 cm x 13.2 cm x 4.4 cm

V = 1277.76 cm³

Next, we shall convert 1277.76 cm³ to m³.

This can be obtained as follow:

1 cm³ = 1×10¯⁶ m³

Therefore,

1277.76 cm³ = 1277.76 × 1×10¯⁶

1277.76 cm³ = 1.27776×10¯³ m³

Therefore, 1277.76 cm³ is equivalent to 1.27776×10¯³ m³.

Next, we shall convert 1562.0 g to kg. This can be obtained as follow:

1000 g = 1 kg

Therefore,

1562.0 g = 1562/1000 = 1.562 kg

Therefore, 1562.0 g is equivalent to 1.562 Kg.

Finally, we shall determine the density of rectangular block as follow:

Volume = 1.27776×10¯³ m³.

Mass = 1.562 Kg.

Density =?

Density = mass /volume

Density = 1.562 / 1.27776×10¯³

Density = 1222.45 Kg/m³

Therefore, the density of rectangular block is 1222.45 Kg/m³

Answer:

a

e(k) =  \frac{2a}{c}  *  sin (\frac{k*a}{2} )

b

G_{v} =  \frac{d e(k ) }{dk }  =  \frac{a^2}{c}  *  cos (\frac{k* a}{2} )

Explanation:

From the question we are told that

    The  velocity  of transverse waves in a crystal of atomic separation is  

                  [tex]b_y  = c \frac{sin (\frac{k*a}{2} )}{\frac{k*a}{2} }[/tex]

Generally the dispersion relation is mathematically represented as

            [tex]e(k) =  b_y  *  k[/tex]

=>    [tex]e(k) = c  \frac{sin(\frac{k*a}{2} ) }{ \frac{k*a}{2} }  *  k[/tex]

=>    [tex]e(k) =   c *  \frac{sin (\frac{k_a}{2} )}{ \frac{a}{2} }[/tex]

=>    [tex]e(k) =  \frac{2a}{c}  *  sin (\frac{k*a}{2} )[/tex]

Generally the group velocity is mathematically represented as

          [tex]G_{v} =  \frac{d e(k ) }{dk }  =  \frac{a^2}{c}  *  cos (\frac{k* a}{2} ) [/tex]

Answer:

The total distance of the truck is 14.6 km

The magnitude and direction of truck's disaplacement is 4 km east

Explanation:

Distance is the total path covered by the trcuk regardless of the direction since distance is described by magnitude only.

The total distance traveled by the truck is given by;

Total Distance = 1.9 km + 9.3 km + 3.4 km

Total Distance = 14.6 km

Displacement is the change in postion at a time interval. In dispalcement direction is considered.

let eastward motion be positive

let westward motion be negative

Displacement = 1.9km east - 9.3 km west + 3.4 km east

Displacement = -4 km east

Therefore, the magnitude and direction of dispalcement = 4 km east