Answer:
The value is [tex]F = 562.7 \ N[/tex]
Explanation:
From the question we are told that
The diameter is [tex]d = 10 \ mm = 0.01 \ m[/tex]
The distance between the poles is L = 50 m
The velocity of the wind is [tex]v = 34 \ m/s[/tex]
Generally the horizontal force the cable puts on each other is mathematically represented as
[tex]F = \frac{1}{2} * C_D * \rho * v^2 * A[/tex]
Here A is the area of the rope(i.e assuming the rope to be a cylinder ) which is mathematically represented as
[tex]A = L * d[/tex]
=> [tex]A = 0.01 * 50[/tex]
=> [tex]A = 0.5[/tex]
Here [tex]C_D[/tex] is the coefficient of discharge of the rope and the value is [tex]C_D = 1.5[/tex]
[tex]\rho[/tex] is the density of air with value [tex]\rho = 1.225 \ kg/m^3[/tex]
So
[tex]F = \frac{1}{2} * C_D * \rho * v^2 * A[/tex]
=> [tex]F = \frac{1}{2} * 1.5 * 1.225 * 34^2 * 0.5[/tex]
=> [tex]F = 562.7 \ N[/tex]
en the current in one coil changes at a rate of 3.2 A/s, an emf of 5.7 is induced in a second, nearby coil. What is the magnitude of the mutual inductance of the two coils
Given that,
The rate of change of current = 3.2 A/s
Emf induced in the coil = 5.7 V
To find,
The magnitude of the mutual inductance of the two coils.
Solution,
The mutual inductance between the coils is given by the formula as follows :
[tex]\epsilon=M\dfrac{dI}{dt}\\\\M=\dfrac{\epsilon}{\dfrac{dI}{dt}}\\\\M=\dfrac{5.7}{3.2}\\\\=1.78\ H[/tex]
So, the mutual inductance of the two coils is 1.78 H.
The mass of an electron is 9.11 x 10-31 kg. If you want to increase the speed of the
electron from 90% of the speed of light to 95% of the speed of light (where the
speed of light is 2.997x108 m/s), the amount of work that must be done is:
8.2 x 10-13)
0 3.2× 10-13 ,
O 2.6% 10-13 ,
O 7.4× 10-14 ,
3.8 x 10-15)
I'm not sure of this question, yet i know you may get angry but, just know your loved and if going through a hard time i'm so so sorry, i know how it feels it sucks. take care of yourself, drink water, listen to that one song that makes you dance in your room and go do what YOU love. your beautiful your perfect and dont listen to what anyone says. i love u, everyone loves u, i know its scary but it happens to everyone life isnt a peice of cake unfortunatly and it sucks but woahh your strong! if you need someone to talk to leave a comment below, happy hoildays everyone!
P.S, im looking into the answer of this question. I may not answer it right on time (since i'm not the smartest...) but i promise ill try my best! Also, i am not doing this for points im doing this to make others smile. I hate how no one checks up on anyone, lots of people are going through a stressful time (including me) and i just want to let everyone know that its okay not to be okay! I hope that you all find happiness in every possible situation, once again HAPPY HOLIDAYS!
19 "Made mostly of ice", fits best under which heading in the table below?
Asteroid
Meteor
Comet
Planet
Description
A Asteroid
B Meteor
C Comet
D Planet
if A.B=A.C
does this imply that B must be equal to c ?
I need answer with example please
Answer:
Yes
Explanation:
[tex]Consider\ three\ variables\ a,b\ and\ c.\\If,\\ab=ac\\a*b=a*c\\We\ may\ now\ divide\ the\ LHS\ and\ RHS\ by\ a,\\Hence,\\\frac{a*b}{a} =\frac{a*c}{a}\\Hence,\\b=c[/tex]
[tex]Ex: \\Consider\ a=5, b=6.\\Hence\ if,\\a*b=a*c\\5*6=5*c\\Hence,\\30=5c\\Hence, c=\frac{30}{5}\\c=6\\As\ b\ also\ equals\ to\ 6,\\b=c[/tex]
a sphere with a radius of 8cm carries a uniform volume charge density of 1.5 find the magnitude of the electric field
Answer:
E = 5.65 x 10¹⁰ N/C
Explanation:
First we need to find the total charge on the sphere. So, we use the following formula for that purpose:
[tex]q = \sigma V\\[/tex]
where,
q = total charge on sphere
V = Volume of Sphere = [tex]\frac{4}{3} \pi r^3 = \frac{4}{3} \pi (0.08\ m)^3 = 0.335\ m^3[/tex]
σ = volume charge density = 1.5 C/m³
Therefore,
[tex]q = (0.335\ m^3)(1.5\ C/m^3) \\q = 0.502 C[/tex]
Now, we use the following formula to find the electric field due to this charged sphere:
[tex]E = \frac{kq}{r^2}[/tex]
where.
E = Electric Field Magnitude = ?
k = Coulomb's Constant = 9 x 10⁹ N.m²/C²
r = radius of sphere = 8 cm = 0.08 m
Therefore,
[tex]E = \frac{(9\ x\ 10^9\ Nm^2/C^2)(0.502 C)}{(0.08\ m)^2}\\\\[/tex]
E = 5.65 x 10¹⁰ N/C
Alex kicks a soccer ball with a force of 250 N. The force is applied to the soccer ball for 0.05 seconds. What is the impulse applied to the ball?
Answer:
12.5 Ns.
Explanation:
From the question given above, the following data were obtained:
Force (F) = 250 N.
Time (t) = 0.05 s
Impulse =?
Impulse can be obtained by using the following formula:
Impulse = force × time
Impulse = 250 × 0.05
Impulse = 12.5 Ns
Thus, the Impulse applied to the ball is 12.5 Ns.
0.0884 moles of a diatomic gas
are in a piston. When the piston
is compressed, the temperature
drops by 18.8 K, and 83.7 J of
heat flow out. Find W.
(Be careful with + and - signs.
+W = expansion, +Q = added,
+AU = temp goes up)
(Unit = J)
Answer:
W = - 118.24 J (negative sign shows that work is done on piston)
Explanation:
First, we find the change in internal energy of the diatomic gas by using the following formula:
[tex]\Delta\ U = nC_{v}\Delta\ T[/tex]
where,
ΔU = Change in internal energy of gas = ?
n = no. of moles of gas = 0.0884 mole
Cv = Molar Specific Heat at constant volume = 5R/2 (for diatomic gases)
Cv = 5(8.314 J/mol.K)/2 = 20.785 J/mol.K
ΔT = Rise in Temperature = 18.8 K
Therefore,
[tex]\Delta\ U = (0.0884\ moles)(20.785\ J/mol.K)(18.8\ K)\\\Delta\ U = 34.54\ J[/tex]
Now, we can apply First Law of Thermodynamics as follows:
[tex]\Delta\ Q = \Delta\ U + W[/tex]
where,
ΔQ = Heat flow = - 83.7 J (negative sign due to outflow)
W = Work done = ?
Therefore,
[tex]-83.7\ J = 34.54\ J + W\\W = -83.7\ J - 34.54\ J\\[/tex]
W = - 118.24 J (negative sign shows that work is done on piston)
Answer:
-49.2
Explanation:
Trust me bro
the question is in a picture
Answer:
same for all objects
Explanation:
earth pulls every object by same force of gravity
a pendulum oscillates 25 times in 5 seconds calculate itrs time period and frequency
Answer:
I. Time period = 0.2 seconds.
II. Frequency = 5 Hertz.
Explanation:
Given the following data;
Time, t = 5 seconds.
Number of oscillation, n = 25 times
I. To find the time period;
[tex] Time \; period = \frac {time}{number \; of \; oscillations}[/tex]
Substituting into the equation, we have;
[tex] Time \; period = \frac {5}{25}[/tex]
Time period = 0.2 seconds.
II. To find frequency;
[tex] Frequency = \frac {1}{Time \; period}[/tex]
Substituting into the equation, we have;
[tex] Frequency = \frac {1}{0.2}[/tex]
Frequency = 5 Hertz.
Therefore, the time period and frequency of the pendulum is 0.2 seconds and 5 Hertz respectively.
Given the data in the question;
Number of oscillation in time t; [tex]n = 25[/tex]
Time taken for the oscillation; [tex]t = 5s[/tex]
Time period
Using the expression for Time period:
[tex]Time \ period = \frac{t}{Number\ of\ oscillation}[/tex]
We substitute our given value into the equation
[tex]Time \ period = \frac{5s}{25}\\\\Time \ period = 0.2s[/tex]
Hence, the time period is 0.2 seconds
Also, using the formula for frequency:
[tex]f = \frac{1}{T}[/tex]
Where f is frequency and T is time period.
We substitute our values into the equation
[tex]f = \frac{1}{0.2s} \\\\f = 5s^{-1}\\\\f = 5Hz[/tex]
Therefore, the frequency of the pendulum is 5 Hertz.
Learn more: https://brainly.com/question/24159297
A particle is moving with (SHM) of period 8.0s and amplitude5.0m
Find
The speed of the particle when it is 3.0m from the centre of it's motion,
The maximum speed,
The maximum acceleration
Answer:
[tex]velocity(x)=15\,\frac{\pi}{4}\,cos(\frac{\pi}{4}x)[/tex]
Max speed = [tex]\frac{15\, \pi}{4} \,\, \frac{m}{s}[/tex]
Max acceleration = [tex]\frac{15\,\pi^2}{16} \,\,\frac{m}{s^2}[/tex]
Explanation:
Given the description of period and amplitude, the SHM could be described by:
[tex]f(x)=5\,sin(\frac{\pi}{4}x)[/tex]
and its angular velocity can be calculated doing the derivative:
[tex]f(x)=5\, \,sin(\frac{\pi}{4}x)\\f'(x)=5\,\frac{\pi}{4}\,cos(\frac{\pi}{4}x)[/tex]
And therefore, the tangential velocity is calculated by multiplying this expression times the radius of the movement (3 m):
[tex]velocity(x)=15\,\frac{\pi}{4}\,cos(\frac{\pi}{4}x)[/tex] and is given in m/s.
Then the maximum speed is obtained when the cosine function becomes "1", and that gives:
Max speed = [tex]\frac{15\, \pi}{4} \,\, \frac{m}{s}[/tex]
The acceleration is found from the derivative of the velocity expression, and therefore given by:
[tex]acceleraton(x)=-15\,\frac{\pi^2}{16}\,sin(\frac{\pi}{4}x)[/tex]
and the maximum of the function will be obtained when the sine expression becomes "-1", which will render:
Max acceleration = [tex]\frac{15\,\pi^2}{16} \,\,\frac{m}{s^2}[/tex]
Which is the luminous object?
In a car, how does an air bag minimize the force acting on a person during a collision?
Answer:
It increases the time it takes for the person to stop.
Explanation:
Answer:
C: It increases the time it takes for the person to stop.
Explanation:
on edge! hope this helps!!~ o(〃＾▽＾〃)o
Conveyor belts are often used to move packages around warehouses. The conveyor shown below moves packages at a steady 4.0 m/s. A 500 N employee decides to catch a ride by sitting on a 1,000 N box for a 50 m trip as shown below:
What is the work done by the employee on the box?
Answer:
0 j
Explanation:
The work done by the employee on the box at the given zero displacement is 0 J.
The given parameters;
Constant velocity of the conveyor, v = 4 m/sWeight of the employee, W = 500 NWeight of the box, W = 1,000 NDistance of the trip, h = 50 mThe work done by the employee on the box is calculated as follows;
W = Fd
where;
F is the applied force on the box by employee = weight of the employeed is the distance through which the box is movedSince the employee sits on the box without moving it, the distance moved by the box = 0
W = 500 x 0
W = 0 J
Thus, the work done by the employee on the box is 0 J.
Learn more about work done and displacement here: https://brainly.com/question/8635561
A force F=9 N acting on a tooth is not in the direction of the tooth axis and runs at a distance L=1 mm from the axis. Find the torque on the tooth about point C
Answer:
τ = 0.009 Nm
Explanation:
The torque applied on the tooth can be given by the following formula:
[tex]\tau = Fd[/tex]
where,
τ = Torque on the tooth= ?
F = Force acting on tooth = 9 N
d = distance between force and tooth axis = 1 mm = 0.001 m
Therefore, using these values in the equation, we get:
[tex]\tau = (9\ N)(0.001\ m)[/tex]
τ = 0.009 Nm
A light wave passes through an aperture (that is, a narrow slit). When it does so, the degree to which the wave spreads out will be...
Explanation:
Single slit diffraction
Diffraction is the phenomenon of spreading out of waves as they pass through an aperture or around objects. Diffraction occurs when the size of the aperture or obstacle is of the same order of magnitude as the wavelength of the incident wave. For very small aperture sizes, the vast majority of the wave is blocked. in case of large apertures the wave passes by or through the obstacle without any significant diffraction.
An image is a copy of an objecí formed by what light
Answer:
Plane mirror
Explanation:
A virtual image is a copy of an object formed at the location from which the light rays appear to come.
A crate of oranges on a horizontal floor has a mass of 30 kg. The coefficient of static friction is 0.62. The coefficient of kinetic friction is 0.52. The worker pulls the crate with a force of 200 N.
What is the equation to calculate the kinetic friction?
What is the kinetic friction on the crate?
Answer:
[tex]Fr_k=152.88\ N[/tex]
Explanation:
Net Force
The net force is defined as the vector sum of all the forces acting on a body at a certain moment.
We should recall some basic concepts and equations to solve the problem.
If no external forces are applied in the vertical direction, the weight of the object and the normal force have the same magnitude and point to opposite directions.
The friction force is defined as:
[tex]Fr_k=\mu_k N[/tex]
[tex]Fr_s=\mu_s N[/tex]
Where the subindices k and s are referred as to the kinetic and static friction forces respectively.
The condition for the object to move is that the applied force is greater than the friction force.
The crate of oranges has a mass of 30 Kg, thus its weight is:
W = m.g = 30 * 9.8 = 294 N
The normal force is:
N = W = 294 N
The kinetic friction is calculated as:
[tex]Fr_k=0.52* 294[/tex]
[tex]\mathbf{Fr_k=152.88\ N}[/tex]
Solenoid 2 has twice the radius and six times the number of turns per unit length as solenoid 1. The ratio of the magnetic field in the interior of 2 to that in the interior of 1 is: 1/3 1 2 4 6
Answer:
6
Explanation:
The magnetic field inside a solenoid is given by the following formula:
[tex]B = \mu_{0}nI[/tex]
where,
B = Magnetic Field Inside Solenoid
μ₀ = permittivity of free space
n = No. of turns per unit length
I = Current Passing through Solenoid
For Solenoid 1:
[tex]B_{1} = \mu_{0}n_{1}I ------------------- equation 1[/tex]
For Solenoid 2:
n₂ = 6n₁
Therefore,
[tex]B_{1} = \mu_{0}n_{2}I\\B_{1} = 6\mu_{0}n_{1}I ----------------- equation 2[/tex]
Diving equation 1 and equation 2:
[tex]\frac{B_{2}}{B_{1}} = \frac{6\mu_{0}nI}{\mu_{0}nI}\\\\\frac{B_{2}}{B_{1}} = 6[/tex]
Hence, the correct option is:
6
The ratio of the magnetic fields in interior 2 to interior 1 will be
[tex]\dfrac{B_2}{B_1} =\dfrac{6}{1}[/tex]
What will be the ratio of the magnetic fields?The formula for the magnetic fields inside the solenoid will be given:
[tex]B=\mu_onI[/tex]
here,
B = Magnetic Field Inside Solenoid
μ₀ = permittivity of free space
n = No. of turns per unit length
I = Current Passing through Solenoid
For the first Solenoid
[tex]B_1=\mu_on_1I[/tex]..................(1)
For the second solenoid
[tex]n_2=6n_1[/tex]
Now
[tex]B_2=\mu_on_2I[/tex]
[tex]B_2=\mu_o(6n_1)I[/tex]..................(2)
Diving equation 1 and equation 2:
[tex]\dfrac{B_2}{B_1} =\dfrac{\mu_o(6n_1)I}{\mu_on_2I}[/tex]
[tex]\dfrac{B_2}{B_1} =6[/tex]
Thus the ratio of the magnetic fields in interior 2 to interior 1 will be
[tex]\dfrac{B_2}{B_1} =\dfrac{6}{1}[/tex]
To know more about the Magnetic field of solenoids follow
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HELP PLEASE
When a magnet spins in a oil of wire it generates
A. Magnetism
B.convection
C. Radiation
D.electricity
Answer:
A, Magnetism
Explanation:
An ordinary electric generator produces electric power by spinning a strong magnet inside a set of wire coils. As the magnet spins, its magnetic field sweeps across the coils and gives rise to electric fields in those coils.
Hope this helps!!
Choose the correct answer
Answer:
1.(c) 7
2.(d) 900
3.(b) two
4.(c) 0.0007
5.(d)0.0004
Explanation:
(1) White light after reflection through prism splits into 7 colors.
(2) Arabs and Chinese knew about lenses in about 900 AD
(3) There are Two more colors in the spectrum which cannot be seen with naked eye.
(4) Wavelength of red light is 0.0007mm
(5) Wavelength of violet light is 0.0004mm
What kinds of forces can act on an object
Two students (90.0 kg and 60.0 kg) on roller skates face-to-face push against each other. The 90.0 kg student moves at 5.0 m/s just after their hands lose contact. What is the velocity of the other student?
Given that,
Mass of student 1, m₁ = 90 kg
Mass of student 2, m₂ = 60 kg
Speed of student 1, v₁ = 5 m/s
To find,
The velocity of the other student.
Solution,
Using the conservation of momentum to find the velocity of the other student. Let it is v₂.
[tex]m_1v_1=m_2v_2\\\\v_2=\dfrac{m_1v_1}{m_2}\\\\v_2=\dfrac{90\times 5}{60}\\\\=7.5\ m/s[/tex]
So, the velocity of the other student is 7.5 m/s.
In a house, 3 bulbs of 60 watt each are lighted for 3 hours daily, 4 fans of 100 watt each are used for 8 hours daily and an electric heater of 2 kwh used for half an hour daily. Calculate the total energy consumed in a month of 31 days and its cost at the rate of Rs 4/kwh.
Answer:
Total Energy consumed = 146.94 kwh
Total cost = rs 587.76
Explanation:
Given:
3 bulbs each 60 watt [for 3 hours daily]
4 fans each 100 watt [for 8 hours daily
1 electric heater of 2 kWh (2,000 watt) [for half hour daily ]
Rate = rs 4/Kwh
Find:
Total Energy consumed
Total cost
Computation:
Energy used = Power × time
3 bulbs each 60 watt [for 3 hours daily] = 3 x 60 x 3 x 31 = 16,740 watt = 16.74 kw
4 fans each 100 watt [for 8 hours daily = 4 x 100 x 8 x 31 = 99,200 watt = 99.2 kw
1 electric heater of 2 kWh [for half hour daily ] = 1 x 2000 x (1/2) x 31 = 31,000 watt = 31 kw
Total Energy consumed = 16.74 + 99.2 + 31
Total Energy consumed = 146.94 kwh
Total cost = 146.94 x 4
Total cost = rs 587.76
What is the power output in watts and horsepower of a 70.0-kg sprinter who accelerates from rest to 10.0 m/s in 3.00 s
Given that,
Mass of a sprinter = 70 kg
Initial velocity, u = 0
Final velocity, v = 10 m/s
Time, t = 3 s
To find,
Power output.
Solution,
The work done by the sprinter is equal to its kinetic energy.
[tex]W=\dfrac{1}{2}m(v^2-u^2)\\\\=\dfrac{1}{2}\times 70\times 10^2\\\\=3500\ J[/tex]
Let P is power output. Power is equal to work done per unit time. So,
[tex]P=\dfrac{3500\ J}{3\ s}\\\\=1166.67\ W[/tex]
So, the power output is 1166.66 W.
PLZZZ I will give brainliest. A ball that contains mechanical energy is rolled across the floor. You notice the ball is slowing down. If the ball started with 20 units of energy, explain how much energy would there be when the ball comes to a complete stop? How can you tell?
Answer: because of friction it will stop rolling completly
Explanation:
A 0.50 mº gas tank holds 3.0 moles of ideal monatomic Helium gas at a temperature of 250 K. What is the mms speed of the molecules? (The Boltzmann constant is 1.38 x 10-23 J/K, NA = 6.022 x 1023 molecules/mol.)
Answer:
v = 1247.92 m/s
Explanation:
The formula for kinetic energy is given as follows:
[tex]K.E = \frac{1}{2}mv^2[/tex]
Another formula that is used for Kinetic Energy is given as:
[tex]K.E = \frac{3}{2}KT[/tex]
Comparing both formulae for K.E:
[tex]\frac{1}{2}mv^2 = \frac{3}{2}KT\\\\mv^2 = 3KT\\v = \sqrt{ \frac{3KT}{m}}[/tex]
where,
v = rms speed of helium molecule = ?
K = Boltzmann Constant = 1.38 x 10⁻²³ J/k
T = Absolute Temperature = 250 K
m = mass of helium molecule = 6.646 x 10⁻²⁷ kg
Therefore,
[tex]v = \sqrt{\frac{(3)(1.38\ x\ 10^{-23}\ J/k)(250\ k)}{6.646\ x\ 10^{-27}\ kg}} \\\\[/tex]
v = 1247.92 m/s
The two ends of an iron rod are maintained at different temperatures. The amount of heat that flows through the rod by conducting DOES NOT depend on
Answer:
D mass of the iron rod
Explanation:
A) the length of the iron rod.
B) the thermal conductivity of iron.
C) the temperature difference between the ends of the rod.
D) the mass of the iron rod.
E) the duration of the time interval
The amount of heat that will flow through an iron rod whose two ends are maintained at different temperatures would depend on the thermal conductivity of the iron, the temperature difference between the two ends, the length of the iron rod, and the duration of flow of heat.
The thermal conductivity of any material is an indication of the ability of the materials to conduct heat. The higher the thermal conductivity, the higher the amount of heat a material can conduct within a specified period. Hence, the amount of heat that will flow through the iron rod depends on its thermal conductivity.
The temperature difference between two solid materials depends on the amount of heat that will flow across the materials by conduction. The higher the difference, the more the amount of heat that will flow. Hence, the amount of heat that would be conducted depends on the temperature difference between the two ends of the iron rod
The amount of heat that would move my conduction also depends on the distance that would be traveled by the heat. Due to heat loss to the surrounding, the shorter the distance, the more the heat and vice versa. Hence, the amount of heat that will flow through an iron rod depends on the length of the iron rod.
The duration of flow also dictates the amount of heat that will flow between two regions by conduction. The more the duration, the more the heat, provided that other conditions remain constant.
The only option that the amount of heat that would be conducted does not depend on is the mass of the iron rod.
The correct option is D.
Elizabeth was a brilliant lawyer until she began hearing voices and seeing things that are not there. She also has trouble with her thought processes and making sense in her speech. She is suffering from:
A. fugue
B. schizophrenia
C. anxiety
D. dissociation
Answer:
B) Schizophrenia
Explanation:
Hope this helps!
At 3.00 m from a source that is emitting sound uniformly in all directions, the sound level (b) is 60.0 dB.
How many meters from the source would the sound level be one-fourth the sound level at 3.00 m?
Given that,
At 3.00 m from a source that is emitting sound uniformly in all directions, the sound level is 60.0 dB.
To find,
The distance from the source would the sound level be one-fourth the sound level at 3.00 m.
Solution,
The intensity from a source is inversely proportional to the distance.
Let I₁ = 60 dB, r₁ = 3 m, I₂ = 60/4 = 15 dB, r₂ =?
Using relation :
[tex]\dfrac{I_1}{I_2}=\dfrac{r_2^2}{r_1^2}\\\\r_2^2=\dfrac{I_1r_1^2}{I_2}\\\\r_2^2=\dfrac{60\times (3)^2}{15}\\\\r_2=6\ m[/tex]
So, at a distance of 6 m the sound level will be one fourth of the sound level at 3 m.
Alex, parked by the side of an east-west road, is watching car P, which is moving in a westerly direction. Barbara, driving east at a speed 52 km/h, watches the same car. Take the easterly direction as positive. If Alex measures a speed of 78 km/h for car P, what velocity will Barbara measure?
Answer:
[tex]v_{PB} = 130\ km/h[/tex]
Explanation:
Since, Alex is at rest. Therefore, the speed measured by him will be the absolute speed of car P. Therefore, taking easterly direction as positive:
[tex]Absolute\ Velocity\ of\ Car\ P = v_{P} = -78\ km/h[/tex]
And the absolute velocity of Barbara's Car is given as:[tex]Absolute\ Velocity\ of\ Barbara's\ Car = v_{B} = 52\ km/h[/tex]
Now, for the velocity of Car p with respect to the velocity of Barbara's Car can be given s follows:
[tex]Velocity\ of\ Car\ P\ measured\ by\ Barbara = v_{PB} = v_{B}-v_{P}\\\\v_{PB} = 52\ km/h-(-78\ km/h)[/tex]
[tex]v_{PB} = 130\ km/h[/tex]