Answer:
5) 4.00, 2.00, 1.0
Explanation:
wave equation is given as;
F₀ = V / λ
Where;
F₀ is the fundamental frequency = first harmonic
Length of the string for first harmonic is given as;
L₀ = (¹/₂) λ
λ = 2 L₀
when L₀ = 1
λ = 2 x 1 = 2m
when L₀ = 2m
λ = 2 x 2 = 4m
For First harmonic, the wavelength is 2m, 4m
For second harmonic;
L₁ = (²/₂)λ
L₁ = λ
When L₁ = 1
λ = 1 m
when L₁ = 2
λ = 2 m
For second harmonic, the wavelength is 1m, 2m
Thus, the wavelength that could represent harmonics present on both strings is 4m, 2m, 1 m
Each wheel of a 320 kg motorcycle is 52 cm in diameter and has rotational inertia 2.1 kg m2 . The cycle and its 75 kg rider are coasting at 85 km/h on a flat road when they encounter a hill. If the cycle rolls up the hill with no applied power and no significant internal friction, what vertical height will it reach
Answer:
The value is [tex]h = 32.91 \ m[/tex]
Explanation:
From the question we are told that
The diameter of each wheel is [tex]d = 52 \ cm = 0.52 \ m[/tex]
The mass of the motorcycle is [tex]m = 320 \ kg[/tex]
The rotational kinetic inertia is [tex]I = 2.1 \ kg \ m^2[/tex]
The mass of the rider is [tex]m_r = 75 \ kg[/tex]
The velocity is [tex]v = 85 \ km/hr = 23.61 \ m/s[/tex]
Generally the radius of the wheel is mathematically represented as
[tex]r = \frac{d}{2}[/tex]
=> [tex]r = \frac{0.52}{2}[/tex]
=> [tex]r = 0.26 \ m[/tex]
Generally from the law of energy conservation
Potential energy attained by system(motorcycle and rider ) = Kinetic energy of the system + rotational kinetic energy of both wheels of the motorcycle
=> [tex]Mgh = \frac{1}{2} Mv^2 + \frac{1}{2} Iw^2 + \frac{1}{2} Iw^2[/tex]
=> [tex]Mgh = \frac{1}{2} * Mv^2 + Iw^2[/tex]
Here [tex]w[/tex] is the angular velocity which is mathematically represented as
[tex]w = \frac{v }{r }[/tex]
So
[tex]Mgh = \frac{1}{2} * Mv^2 + I \frac{v}{r} ^2[/tex]
Here [tex]M = m_r + m[/tex]
[tex]M = 320 + 75[/tex]
[tex]M = 395 \ kg[/tex]
[tex]395 * 9.8 * h = 0.5 * 395 * (23.61)^2 + 2.1 *[\frac{ 23.61}{ 0.26} ] ^2[/tex]
=> [tex]h = 32.91 \ m[/tex]
If you unbend a paper clip made from 1.5 millimeter diameter wire and push one end against the wall, what force must you apply to give a pressure of 120 atmospheres
Answer:
The force is [tex]F = 21.48 \ N[/tex]
Explanation:
From the question we are told that
The diameter of the wire is [tex]d = 1.5 \ mm = 1.5 *10^{-3} \ m[/tex]
The pressure is [tex]P = 120 \ a.t.m = 120 * 101.3 *10^{3} = 12156000 Pa[/tex]
Generally the radius of the of the wire is
[tex]r = \frac{d}{2}[/tex]
=> [tex]r = \frac{ 1.5 *10^{-3}}{2}[/tex]
=> [tex]r = 7.5 *10^{-4} \ m[/tex]
The Area is evaluated as
[tex]A = \pi r^2[/tex]
=> [tex]A = 3.142 * 7.5 *10^{-4}[/tex]
=> [tex]A = 1.7673*10^{-6} \ m^2[/tex]
Generally pressure is mathematically represented as
[tex]P = \frac{F}{A }[/tex]
=> [tex]F = P* A[/tex]
=> [tex]F = 12156000 * 1.767*10^{-6}[/tex]
=> [tex]F = 21.48 \ N[/tex]
A tire swing hanging from a branch reaches nearly to the ground. How could you estimate the height of the branch using only a stopwatch?
Answer:
A stop watch measures time and the number of seconds making an osculation is the period T
Which is T = 2π√(L/g)........solving for L (the length of the pendulum),
Then the L = T²x g/( 4πr²) substitute and then u find length or height of the swing
A grating has 320 lines/mm. How many orders of the visible wavelength 551 nm can it produce in addition to the m = 0 order
Answer:
6
Explanation:
Given that
dsinθ = mλ,
now, if sinθ = 1, then
m = d / λ, where
m = order of interference
d = distance between the slits
λ = wavelength of light
this is the formula we would use to solve the question
d = 1 / 320 lines/mm
d = 1 / 320*10^3
d = 3.125*10^-6 m
At λ = 551 nm, we have
m = 3.125*10^-6 / 551*10^-9
m = 5.67
5.67 ~ 6
thus, we can say that the orders of visible wavelength 551 nm, can produce is 6
The floor of a railroad flatcar is loaded with loose crates having a coefficient of static friction of 0.420 with the floor. If the train is initially moving at a speed of 57.0 km/h, in how short a distance can the train be stopped at constant acceleration without causing the crates to slide over the floor
Answer:
The distance is [tex]s= 30.3 \ m[/tex]
Explanation:
From the question we are told that
The coefficient of static friction is [tex]\mu_s = 0.42[/tex]
The initial speed of the train is [tex]u = 57 \ km /hr = 15.8 \ m/s[/tex]
For the crate not to slide the friction force must be equal to the force acting on the train i.e
[tex]-F_f = F[/tex]
The negative sign shows that the two forces are acting in opposite direction
=> [tex]mg * \mu_s = ma[/tex]
=> [tex]-g * \mu_s = a[/tex]
=> [tex]a = -9.8 * 0.420[/tex]
=> [tex]a = -4.116 m/s^2[/tex]
From equation of motion
[tex]v^2 = u^2 + 2as[/tex]
Here v = 0 m/s since it came to a stop
=> [tex]s= \frac{v^2 - u^2 }{ 2 a}[/tex]
=> [tex]s= \frac{0 -(15.8)^2 }{ - 2 * 4.116}[/tex]
=> [tex]s= 30.3 \ m[/tex]
Suppose no stars more massive than about 2 solar masses had ever formed. Would life as we know it have been able to develop
Answer:
No, life would not be to develop
Explanation:
Stars less massive than about 2 solar masses can only produce natural element up to carbon and oxygen, which are the basic elements for building life. However, other more massive elements are needed by life to thrive and function properly, more massive elements like phosphorus, iron necessary for oxygen circulation, calcium for a strong support system, and silicon are essential for for life to form and be sustained here on Earth.
What does this picture show?
Answer:
d poor accuracy,poor precision
The diagram represents how much accurate and precise the result data is. It is clear from the image that, the data points have poor accuracy and good precision.
What is accuracy ?Accuracy of a result is the measure of the closeness of the experimental or calculated value to the true value or absolute value of a measurement. For a reproducible experiment, the results for each trials can be differ or close.
The closeness between values of a set of experiments is called precision of the results. Not all accurate value be can be precise. Similarly precision of values does not need to meet accuracy.
Here, the central dot indicates the true value. The green points are a set of experimental values. They are not so close to the true value and hence it is less accurate. However, all the points and closer together. Hence, they are precise. Therefore, option B is correct.
Find more on accuracy:
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A 1.5m wire carries a 7 A current when a potential difference of 87 V is applied. What is the resistance of the wire?
Answer:
Ohm's law states that I=V/R (Current=volts divided by resistance). Since we're looking for resistance, we'll rewrite it as R=V/I. Then just plug in the numbers; R=84/9, R= 9 1/3 or 28/3. The resistance of the wire is 9.33... or 9 1/3 ohm's, depending on how you wanna write it.
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
I would appreciate it!
Answer:
[tex]R\approx12.43 \,\, \Omega[/tex]
Explanation:
We can use Ohm's Law to find the resistance R of a wire that carries a current I under a given potential difference:
[tex]V=I\,\,R\\R = \frac{V}{I} \\R=\frac{87}{7} \\R\approx12.43 \,\, \Omega[/tex]
Simple Harmonic Motion: The quartz crystal in a digital watch has a frequency of 32.8 kHz. What is its period of oscillation
Answer:
Time Period of Oscillation = 3.04 x 10⁻⁵ s
Explanation:
The time period of oscillation and the the frequency of oscillation are two inter linked quantities. They are actually the reciprocals of each other. So, the time period of oscillation of quartz crystal is given by the following formula:
Time Period of Oscillation = 1/Frequency of Oscillation
where,
Frequency of Oscillation = 32.8 KHz
Frequency of Oscillation = 32800 Hz
Therefore,
Time Period of Oscillation = 1/32800 Hz
Time Period of Oscillation = 3.04 x 10⁻⁵ s
4. How does the type of medium affect a sound wave?
Answer:
The type of medium affects a sound wave as sound travels with the help of the vibration in particles.
Explanation:
As different mediums have different amount and size of particles, for example, the speed of sound is faster through solid than liquid as solids have closely packed particles whereas liquids are loosely packed.
The speed of sound in a given medium is determined by its density and stiffness (or compressibility in the case of gases).The speed of sound increases with the rigidity (or lack of compressibility) of the medium. The speed of sound decreases with increasing medium density.
What type of medium affect a sound wave?Any material or area through which a wave is transmitted is referred to as a medium. Four variables impact a wave's speed: wavelength, frequency, medium, and temperature. The wavelength and frequency are multiplied to determine the wave speed (speed = l × f).
Therefore, The rate at which energy is transferred through a medium depends on the amplitude of the vibrations of its constituent particles; the higher this rate, the more powerful the sound wave.
Learn more about sound wave here:
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Two vehicles collide and stick together. After the collision, their combined y-momentum is 2.40 × 104 kilogram meters/second, and their x-momentum is 7.00 × 104 kilogram meters/second. What is the angle of the motion of the two vehicles, with respect to the x-axis?
Explanation:
It is given that,
Momentum in y direction is [tex]2.4\times 10^4\ kg-m/s[/tex]
Momentum in x direction is [tex]7\times 10^4\ kg-m/s[/tex]
We need to find the angle of the motion of the two vehicles, with respect to the x-axis. The angle between two vectors is given by :
[tex]\tan\theta=\dfrac{p_y}{p_x}\\\\\tan\theta=\dfrac{2.4\times 10^4}{7\times 10^{4}}\\\\\theta=\tan^{-1}\left(0.342\right)\\\\\theta=18.88^{\circ}[/tex]
So, the angle of the motion of the two vehicles is 18.88 degrees.
A person whose near-point distance is 45.5 cm wears a pair of glasses that are 2.1 cm from her eyes. With the aid of these glasses, she can now focus on objects 25 cm away from her eyes.
Required:
a. Find the focal length of her glasses.
b. Find the refractive power of her glasses.
Answer:
a
[tex]f = 0.4848 \ m[/tex]
b
[tex]p = 2.063 D[/tex]
Explanation:
From the question we are told that
The near point distance is [tex]k = 45.5 \ cm[/tex]
The distance of the glasses from the eye is [tex]y = 2.1 \ cm[/tex]
The distance of an object she can focus with the glass is [tex]i= 25 \ cm[/tex]
Generally the image distance is mathematically evaluated as
[tex]v = -(45.5 - 2.1)[/tex]
[tex]v = -43.4 \ cm[/tex]
Generally the object distance is mathematically represented as
[tex]u = (25 -2.1)[/tex]
[tex]u = 22.9 \ cm[/tex]
The negative sign tells us that the image was formed behind the eye
Generally the lens formula is mathematically represented as
[tex]\frac{1}{f} = \frac{1}{u} + \frac{1}{v}[/tex]
=> [tex]\frac{1}{f} = \frac{1}{22.9} + \frac{1}{ - 43.4}[/tex]
=> [tex]f = 48.48 \ cm[/tex]
converting to meters
[tex]f = 0.4848 \ m[/tex]
Thus the refractive power is mathematically represented as
[tex]p = \frac{1}{f}[/tex]
=> [tex]p = \frac{1}{0.4848 }[/tex]
=> [tex]p = 2.063 D[/tex]
A round pipe of varying diameter carries petroleum from a wellhead to a refinery. At the wellhead, the pipe's diameter is 58.9 cm ( 0.589 m) and the flow speed of the petroleum is 12.1 m/s. At the refinery, the petroleum flows at 6.29 m/s. What is the volume flow rate of the petroleum along the pipe and what is the pipe's diameter at the refinery?
Answer:
Explanation:
The volume rate of flow = a x v where a is cross sectional area of pipe and v is velocity of flow
putting the values
π x .2945² x 12.1
= 3.3 m³ /s
To know the pipe's diameter at the refinery we shall apply the following formula
a₁ v₁ = a₂ v₂
a₁ v₁ and a₂ v₂ are volume rate of flow of liquid which will be constant .
3.3 = a₂ x 6.29
a₂ = .5246 m³
π x r² = .5246
r = .4087 m
= 40.87 cm
diameter
= 81.74 cm
Experts in model airplanes develop a supersonic plane to scale, it moves horizontally in the air while it is conducting a flight test. The development team defines that the space that the airplane travels as a function of time is given by the function: e (t) = 9t 2 - 6t + 3 Determine what acceleration the scale airplane has (Second derivative).
Explanation:
e(t) = 9t² − 6t + 3
The velocity is the first derivative:
e'(t) = 18t − 6
The acceleration is the second derivative:
e"(t) = 18
Which is the property of mattter in which substance can transfer heat to electricity
Conductivity is the property of matter in which a substance can transfer heat or electricity.
Additional information:-Matter : Anything which occupies space and has mass is called matter.
Chemical classifications
Pure Substances ( made of one kind of substance )Impure Substances ( mixture )Physical classifications
Solid Liquid GasPlasma ( made of ions and free electrons )BEC ( Bose Einstein Condensate )Fermionic Condensate ( It discovered in 2003 )The x component of vector is 8.7 units, and its y component is -6.5 units. The magnitude of is closest to
Answer:
F = 10.86 units
Explanation:
The magnitude of a vector in terms of the magnitude of its rectangular components is given by the following formula:
F = √(Fₓ² + Fy²)
where,
F = Magnitude of the Vector = ?
Fₓ = magnitude of the x-component of vector = 8.7 units
Fy = magnitude of y component of vector = - 6.5 units
Therefore, using these values in the equation, we get:
F = √[(8.7 units)² + (- 6.5 units)²]
F = √(117.94 units²)
F = 10.86 units
A lightning bolt with 13 kA strikes an object for 14 μ s. How much charge is deposited on the object?
Answer:
0.182C
Explanation:
Using Q= It
= 13x10^3 . 14x10^-6
= 0.182C
The pressure at the bottom of a full barrel of water is Poriginal . Determine what happens to the pressure when the radius or height of the barrel is changed and water is added to make the barrel full again.
Answer:
a) P' = P_original, b) P ’= P_original + ρ g Δh
Explanation:
The expression for nanometric pressure is
P = ρ g h
where ρ is the density of the liquid and h is the height
a) we change the radius of the barrel, but keeping the same height
as the pressure does not depend on the radius it remains the same
P' = P_original
b) We change the barrel height
h ’≠ h
we substitute in the equation
P ’= ρ g h’
h ’= h + Δh
P ’= ρ g (h + Δh)
P ’= (ρ g h) + ρ g Δh
P ’= P_original + ΔP
In this case, the pressure changes due to the new height,
*if it is higher than the initial one, the pressure increases
*if the height is less than the initial one, the pressure is less
What is the Malebioncy of a Capacitor?
Answer:
The switching rate between the steady state and the normal state of a capacitor
Explanation:
This was a hard one! Could only find it in my textbook. Anyways this basically is the rate which the capacitors switches back from steady state and normal state from when it charges and discharges over time. This has many purposes as a special type of diode or any other transistor type device etc etc.
A large number of very industrious people make a very long pole. It is 10.0 light years long! ( As they measure it. ) Soon a spaceship flies along the length of the pole at 90% the speed of light. How much time passes on the spaceship from the moment the ship passes the first end of the pole to the moment the ship passes the second end of the pole
Answer:
L = L0 ( 1 - v^2/c^2))1/2 where L0 is the proper length
L = 10 L-y (1 - .9^2)^1/2 = 4.36 L-y length of pole measured by ship
t = 4.36 L-y / .9 c = 4.84 y since the ship travels at .9 c
Where are the most reactive elements located on the periodic table.
Answer:
The most reactive elements are at the bottom left corner of the periodic table. Those are the elements that have the most active/most reactive. For example, lithium, sodium, and potassium all react with water!
Explanation:
Don't know what to explain :v
A parachuter, falling with a constant speed, drops 456m in 14.4s.
Determine all unknowns.
S =
51
m/s
d =
456
m
t =
14.4
S
Answer:
The parachuter is falling at a speed of 31.667 meters per second.
Explanation:
Given that parachuter falls at constant speed and travelled distance and time are known, the unknown is speed, measured in meters per second, which is obtained by the following kinematic expression:
[tex]s = \frac{d}{t}[/tex]
Where:
[tex]d[/tex] - Travelled distance, measured in meters.
[tex]t[/tex] - Time, measured in seconds.
If [tex]d = 456\,m[/tex] and [tex]t = 14.4\,s[/tex], the speed of the parachuter is:
[tex]s = \frac{456\,m}{14.4\,s}[/tex]
[tex]s = 31.667\,\frac{m}{s}[/tex]
The parachuter is falling at a speed of 31.667 meters per second.
A particle with charge q and kinetic energy K travels in a uniform magnetic field of magnitude B. If the particle moves in a circular path of radius R, find expressions for:
a. its speed
b. its mass.
Answer:
Given that K.E is
1/2mv²
So to find speed v,
Make it subject
K.E= 1.2mv²
However radial force = magnetic force
So mv²/r= qvB
So v subject
V= 2K.E/ qBr that is speed
To find mass
K.E = 1/2mv²
Puy value of v
So KE= 1/2m(2K.E/qBr)
m= (qBr)/2K.E
That is mass
Answer:
m = qbr/v
v = 2k/qbr
Explanation:
When a charged particle enters a magnetic field, it experiences a force that is always perpendicular to the velocity. This force provides a centripetal force, and thus, we have
qvb = mv²/r
if we make m the subject of the formula, we will have
m = qbr/v
Recall that the kinetic energy, KE = ½mv²
Now, let's make v² the subject of formula, we have
v² = 2K/m
now, we substitute for m from the equation we got earlier
v² = 2K / (qbr/v)
v² = 2Kv / qbr, if we simplify further, we have
v = 2k / qbr
Therefore, we can say that the expression for the mass and speed is respectively,
m = qbr/v
v = 2k/qbr
What is force? What creates it?
Answer:
its an interaction that can move an object; push or pull makes it or gravity, magnetism
Explanation:
its all in the answer
Answer:
In physics, a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object withmass to change its velocity (which includes to begin moving from a state of rest), i.e., toaccelerate.
Which statement about the ocean is true? A. No evaporation or precipitation in the water cycle occurs over the ocean. B. Most evaporation and precipitation in the water cycle occur over the ocean. C. All evaporation and precipitation in the water cycle occur over the ocean. D. Evaporation, but not precipitation, in the water cycle occurs over the ocean.
Answer:
A
Explanation:
Answer:
A
Explanation:
No evaporation or precipitation in the water cycle occurs over the ocean.
6. Solve (5.87 x 10^7)(4.200 x 10^11). Be
sure your answer is in scientific notation.
Round to two decimal places.
Explanation:
We need to solve [tex](5.87\times 10^7)(4.2\times 10^{11})[/tex]
Firstly, multiplying 5.87 and 4.2 = 24.654
Now taking exponent of 10.
We know that : [tex]x^a{\cdot} x^b=x^{a+b}[/tex]
It means, [tex]10^7{\cdot} 10^{11}=10^{11+7}=10^{18}[/tex]
So,
[tex](5.87\times 10^7)(4.2\times 10^{11})=24.654\times 10^{18}[/tex]
In scientific notation,
[tex](5.87\times 10^7)(4.2\times 10^{11})=2.4654\times 10^{19}[/tex]
Hence, the value of [tex](5.87\times 10^7)(4.2\times 10^{11})[/tex] is [tex]2.4654\times 10^{19}[/tex]
Answer:
Explanation:
We need to solve
Firstly, multiplying 5.87 and 4.2 = 24.654
Now taking exponent of 10.
We know that :
It means,
So,
In scientific notation,
Hence, the value of is
For a conductor in electrostatic equilibrium, which of the following properties are true?
a) Any excess charge is uniformly spread throughout the volume of the conductor.
b) The electric field inside is zero.
c) The entire conductor is at the same potential.
Answer:
b) The electric field inside is zero.
Explanation:
This is simply because the charges in the field will be in motion, thus this charges kind of spread around to make the conductor field zero.
uncertainty propagation question #2
Hi all, I am trying to calculate the uncertainty and volume for a rectangular block with the measurements being 8.7cm, 5.2cm, 5.4cm. I am struggling with the uncertainty propagation, and I am unsure if I did this correctly. Heres what I've tried.
I found the uncertainty for each individual measurement to be .1 because they all have 1 decimal place. I Added this to the formula with the measurements, took the square root of the sum of the squares with the uncertainty for each individual measurement being in the numerator and the measurement in the denominator, as follows: √(.1/8.7)\^2 + (.1/5.2)\^2 + (.1/5.4)\^2. My final answer was volume= 244.296 +/- .029 cm\^3. I rounded the uncertainty that I got from the equation to 2 significant figures because that’s what the smallest measurement has. Did I do this correctly?
Answer:
The correct treatment of uncertainties for the volume is shown below
Explanation:
In order to estimate the uncertainty in the volume which is derived via the formula:
[tex]V = w*l*h[/tex]
you normally start with the relative errors [tex](\frac{\delta Q}{Q})[/tex] of each quantity (Q) measured, since they are so easy to handle, stating that the relative error in the Volume is the addition of the relative errors in each quantity:
[tex]\frac{\delta V}{V} =\frac{\delta w}{w} +\frac{\delta l}{l} +\frac{\delta h}{h}[/tex]
and finally solve for [tex]\delta V[/tex] by multiplying both sides by the volume you calculated.
In your case, this becomes:
[tex]\delta V =V \left \{\frac{\delta w}{w} +\frac{\delta l}{l} +\frac{\delta h}{h}\right \} \\\delta V = 244.296 \left \{\frac{0.1}{5.4} +\frac{0.1}{8.7} +\frac{0.1}{5.2}\right \}\\\delta V = 244.296 \, (0.04924354)\\\delta V = 12.03 \,\,cm^3[/tex]
Then, since the standard practice is to write the uncertainty with ONLY ONE significant figure, the rounding of your uncertainty becomes:
[tex]\delta V=10\,\,cm^3[/tex]
Giving this, you need to express the final measurement as:
[tex]V=240\,\,cm^3\,+/- 10 \,\,cm^3[/tex]
making sure that the expression for the volume doesn't have significant figures passed the limitation imposed by its uncertainty (in this case the tenths).
Please notice as well that in the treatment you did, you:
1) ended up with an uncertainty even smaller than the relative uncertainty of each measurement (which cannot be possible since relative uncertainties add-up)
2) are not rounding your uncertainty to ONE SIG FIG.
Find the sum of the following vectors A=3i-12j and B=4i+7j
Answer:
(I). The sum of the vectors is (7i-5j).
(II). The sum of the vectors is (8i+7j).
Explanation:
Given that,
(I). Vector A [tex]A=3i-12j[/tex]
Vector B [tex]B=4i+7j[/tex]
Suppose, (II). Vector A [tex]A=6i+15j[/tex]
Vector B [tex]B=2i-8j[/tex]
(I). We need to calculate the sum of the vectors
Using formula of sum
[tex]\vec{C}=\vec{A}+\vec{B}[/tex]
Where,
[tex]\vec{A}= vector A[/tex]
[tex]\vec{B}= vector B[/tex]
[tex]\vec{C}= sum of the vector A and b
Put the value into the formula
[tex]\vec{C}=(3i-12j)+(4i+7j)[/tex]
[tex]\vec{C}=7i-5j[/tex]
(II). We need to calculate the sum of the vectors
Using formula of sum
[tex]\vec{C}=\vec{A}+\vec{B}[/tex]
Put the value into the formula
[tex]\vec{C}=(6i+15j)+(2i-8j)[/tex]
[tex]\vec{C}=8i+7j[/tex]
Hence, The sum of the vectors is (7i-5j).
The sum of the vectors is (8i+7j).
You drive 6.00 km at 50.0 km/h and then another 6.00kmat 900 km/h Your average speed over
the 12.0 km drive will be
Explanation:
average speed = total distance travelled / total time travelled
time to travel the first 6km: 6 / 50 = 3/25 (h)
time to travel the next 6km: 6 / 90 = 1/15 (h)
[I think there's problem in the question 'cause 900km/h sounds impossible for normal person to travel in normal condition]
The total time: 3/25 + 1/15 = 14/75 (h)
Average speed over the 12 km drive will be:
[tex] \frac{12}{ \frac{14}{75} } = \frac{450}{7} = 64.3 \: km{h}^{ - 1} [/tex]