[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Here,
The projectile is fired with initial velocity =100m/sThe Angle formed with the horizontal = 30°Answer (a)Here, we have
Initial velocity = 100 m/sAngle of projection = 30°We have to find the time of flight
We know that,
Time of flight
[tex]\sf{ = }{\sf{\dfrac{ 2uSin{\theta}}{g}}}[/tex]
Subsitute the required values,
[tex]\sf{ = }{\sf{\dfrac{ 2{\times}100{\times}Sin30{\degree}}{9.8}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{ 200{\times}{\frac{1}{2}}}{9.8}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{ 100}{9.8}}}[/tex]
[tex]\bold{ = 10.20 \: s }[/tex]
Hence, The time of flight is 10.20 sec .
Answer (b)Here, We have
Initial velocity = 100 m/sAngle of projection = 30°We have to find the maximum height attained by the body
We know that,
Maximum height
[tex]\sf{ = }{\sf{\dfrac{ u^{2}Sin^{2}{\theta}}{2g}}}[/tex]
Subsitute the required values,
[tex]\sf{ = }{\sf{\dfrac{ (100)^{2}{\times}Sin^{2}30{\degree}}{2{\times} 9.8}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{ 10000{\times}{\frac{1}{2}}{\times}{\frac{1}{2}}}{19.6}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{ 5000{\times}{\frac{1}{2}}}{19.6}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{ 2500}{19.6}}}[/tex]
[tex]\sf{ = 127.5 \: m}[/tex]
Hence, The maximum height attained by the body is 127.5 .
Answer ( c) :-Here, we have
Initial velocity = 100 m/sAngle of projection = 30°We have to find the horizontal range
We know that,
Horizontal range
[tex]\sf{ = }{\sf{\dfrac{ u^{2}Sin2{\theta}}{g}}}[/tex]
Subsitute the required values,
[tex]\sf{ = }{\sf{\dfrac{ (100)^{2}{\times}Sin2{\times}30{\degree}}{9.8}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{ 10000{\times}Sin{\times}60{\degree}}{9.8}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{ 10000{\times}{\frac{\sqrt{3}}{2}}}{9.8}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{ 5000{\times}\sqrt{3}}{9.8}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{ 5000{\times}1.732}{9.8}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{ 8660}{9.8}}}[/tex]
[tex]\sf{ = 883.67 \: or 883.7 m}[/tex]
Hence, The range of the body is 883.67 or 883.7 m.
Answer:
(a) 10.20 s (nearest hundredth)
(b) 127.55 m (nearest hundredth)
(c) 883.70 m (nearest hundredth)
Explanation:
Part (a)
At the end of the projectile's flight, its vertical displacement will be zero.
Resolving vertically, taking up as positive:
[tex]s=0\quad u=100 \sin30^{\circ} \quad v=v, \quad a=-9.8, \quad t=t[/tex]
[tex]\begin{aligned}\textsf{Using }\:s & =ut+\dfrac12at^2:\\ 0 & =100 \sin 30^{\circ}t+\dfrac12(-9.8)t^2\\ 0 & = 50t-4.9t^2\\ 4.9t^2 & = 50t\\ 4.9t & = 50\\ t & = \dfrac{50}{4.9}\\ t & = 10.20\:\sf s\:(nearest\:hundredth)\end{aligned}[/tex]
Part (b)
At the maximum height, vertical velocity will be zero.
Resolving vertically, taking up as positive:
[tex]s=0\quad u=100 \sin30^{\circ} \quad v=0, \quad a=-9.8, \quad t=t[/tex]
[tex]\begin{aligned}\textsf{Using }\:v^2 & = u^2+2as :\\ 0^2 & = (100 \sin 30^{\circ})^2+2(-9.8)s\\ 0 & = 2500-19.6s\\ 19.6s & = 2500\\ s & = \dfrac{2500}{19.6}\\ s & = 127.55\: \sf m\:(nearest\:hundredth) \end{aligned}[/tex]
Part (c)
The horizontal velocity of a projectile is always constant, so u = v.
The horizontal component of acceleration is zero.
Resolving horizontally, taking right as positive (and using the value for t we found in part a):
[tex]s=s\quad u=100 \cos30^{\circ} \quad v=100 \cos30^{\circ} , \quad a=0, \quad t=\dfrac{50}{4.9}[/tex]
[tex]\begin{aligned}\textsf{Using }\:s & =ut+\dfrac12at^2 : \\ s & =(100 \cos 30^{\circ})\left(\dfrac{50}{4.9}\right)+\dfrac12(0)\left(\dfrac{50}{4.9}\right)^2\\ s & =50\sqrt{3}\left(\dfrac{50}{4.9}\right)+0\\ s & =883.70\: \sf m\:(nearest\:hundredth)\end{aligned}[/tex]
12 Ω resistor and a 15 Ω resistor are connected in series across a 9.0 V potential difference. What is the current in the circuit
The current in the series circuit across a 9.0 V potential difference is determined as 0.333 A.
Current in the series circuit
The current in the series circuit is determined by applying ohms law as shown below;
V = IR
where;
I is the currentR is equivalent resistance of the circuitR = 12 Ω + 15 Ω = 27 Ω
I = V/R
I = 9/27
I = 0.333 A
Thus, the current in the series circuit across a 9.0 V potential difference is determined as 0.333 A.
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A velocity selector for ions uses perpendicular electric and magnetic fields. If the electric field used were 800 V/m, what magnetic field would allow the selection of a velocity of 4000 m/s?
For a velocity selector for ions using perpendicular electric and magnetic fields is mathematically given as
B= 0.225 T
What magnetic field would allow the selection of a velocity of 4000 m/s?
Generally, the equation for the magnetic field is mathematically given as
B = E/v
Therefore
B = 900/4000
B= 0.225 T
In conclusion. the magnetic field is
B= 0.225 T
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Use the Newton's Law Triangle to solve the following problem
A bowling ball had 50 N of force when it accelerated down the lane at a rate of 2m/s2. How much mass did the bowling ball have?
________kilograms
Answer:
The answer would be 25kg.
Explanation:
Because the force is 50 N and the acceleration is 2 meters per second squared and the Newton's Law Triangle is F = m x a or Force = Mass x Acceleration so we have to solve the equation 50 divided by 2 or 50/2 which results in 25kg.
what is the principle of moments?
Answer:
The Principle of Moments states that when a body is balanced, the total clockwise moment about a point equals the total anticlockwise moment about the same point.
Explaining with equation
Moment =force F x perpendicular distance from the pivot d. Moment = Fd.
ease select the word from the list that best fits the definition
equal to mass multiplied by velocity
mpulse
mpulse
mpulse-momentum theorem
nomentum
angular momentum
Relate states of the matter with heat by a proper graph and describe the graph fully by your own words
Answer: If you are adding heat to a sample at a constant rate , you plot the temperature against time.
Explanation:
Two children of mass 18 kg and 29 kg sit balanced on a seesaw with the pivot point located at the center of the seesaw. If the children are separated by a distance of 5 m, at what distance from the pivot point is the small child sitting in order to maintain the balance?
Answer:
3.085 [m].
Explanation:
1) The rule:
m₁*g*l₁=m₂*g*l₂, where m₁ and l₁ - the mass and distance for the small child, m₂ and l₂ - for the big child;
2) according to the condigion l₁+l₂=5, then
3) it is possible to make up the system:
[tex]\left \{ {{l_1+l_2=5} \atop {m_1*l_1=m_2*l_2}} \right. \ = > \ \left \{ {{l_1=5-l_2} \atop {18*(5-l_2)=29*l_2}} \right. \ = > \ \left \{ {{l_1=\frac{145}{47}} \atop {l_2=\frac{90}{47}}} \right.[/tex]
4) finally, l₁=145/47≈3.085 [m].
Calculate the net force on particle q1. First, find the direction of the force particle q2 is exerting on particle 91. Is it pushing to the right (+), or to the left (-)? Enter + or - -5.90 C +13.0 μC +91 93 +7.70 μC + 92 + 0.25 m K 0.30 m
Answer:
(b) from left to right (→)
Explanation:
Frictional Force
When the surface of one object comes into touch with the surface of another, friction is the force that resists motion. Friction reduces a machine’s mechanical advantage, or, to put it another way, friction reduces the output-to-input ratio. Frictional force refers to the force generated by two surfaces that contact and slide against each other.
Friction is caused due to the irregularities on the two surfaces in contact. So, when one object moved over the other, these irregularities on the surface get entangled, giving rise to friction.
The more the roughness, the more irregularities and more significant will be the friction.
Friction always acts in the opposite direction to the motion, hence the force of friction will be from left to right.
. An experimental rocket plane lands on skids on a dry lake bed. If it’s traveling at 80.0 m/s when it touches down, how far does it slide before coming to rest? Assume the coefficient of kinetic friction between the skids and the lake bed is 0.6.
Answer:
1. A substance that can be separated into two or more substances only by a chemical change is a(n) _____.
solution
element
mixture
compound
2.
Which of the following materials is a substance?
air
gasoline
stainless steel
silver
3.
The first figure in a properly written chemical symbol always is _____.
boldfaced
capitalized
italicized
underlined
4.
Which of the following represents a compound?
H
H-3
H2O
O-16
5. What do chemical symbols and formulas represent, respectively?
elements and compounds
atoms and mixtures
compounds and mixtures
elements and ions
Explanation:
The rocket plane will travel 800 meters before coming to rest.
What is stopping distance?initial speed= 80 m/s
kinetic friction= 0.6
Net force action on the plane:
F- kinetic friction = mass * acceleration
mass*g - 0.6*mass*g=mass*acceleration (take g=10m/s)
acceleration=4m/s
calculation of stopping distance:-
V²=U²-2as
0+2as=U²
S=U²/2a
S=(80*80)2*4
S=800 meter.
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#SPJ2
Three loads, of 24 A, 8 A, and 12 A are supplied from a 200 V source. If a motor of resistance 2.4 Ohms is also connected across the supply, calculate (a) the total resistance and (b) the total current drawn from the supply.
Answer:
See below ~
Explanation:
Total Resistance
R₁ (across 24A load) = 200/24 = 8.33 ΩR₂ (across 8A load) = 200/8 = 25 ΩR₃ (across 12A load) = 200/12 = 16.67 ΩR₄ (given) = 2.4 ΩR = R₁ + R₂ + R₃ + R₄R = 8.33 + 25 + 16.67 + 2.4R = 25 + 25 + 2.4R = 50.4 ΩTotal Current Drawn
Source Voltage / Total Resistance200 V / 50.4 Ω3.97 A (To the nearest hundredth)A. The probabilities are decimals, which can never represent a probability. B. Two possible outcomes have an identical probability, which is not possible. C. The sum of all possible moves is greater than 1, which is not possible. D. The probability of two possible outcomes sums to the probability of another outcome, which is not possible.
Answer:
Explanation:
wo possible outcomes have an identical probability, which is not possible. C. The sum of all possible moves is greater than 1, which is not possible. D. The probability of two possible outcomes sums to the probability of another outcome, which is not possible.
5. Two objects of masses 1kg and 2kg respectively are released from rest when their separation is 10 m. assuming that on it mutual gravitational force act on them, find the velocity of each of them when separation becomes 5m.
The velocity of 1kg and 2 kg mass when separation becomes 5m is 1.334 x 10⁻¹¹ m/s and 6.67 x 10⁻¹² m/s respectively.
Force between the massesThe gravitational force between the masses is determined as follows;
[tex]F = \frac{Gm_1m_2}{r^2} \\\\F = \frac{(6.67 \times 10^{-11}) (1)(2)}{10^2} \\\\F = 1.334 \times 10^{-12} \ N[/tex]
Acceleration of each objectsa = F/m
a₁ = (1.334 x 10⁻¹²) / (1)
a₁ = 1.334 x 10⁻¹² m/s²
a₂ = (1.334 x 10⁻¹²) / (2)
a₂ = 6.67 x 10⁻¹³ m/s²
Velocity of each objectv = u + 2ad
v₁ = u₁ + 2a₁d
v₁ = 0 + 2( 1.334 x 10⁻¹² )(5)
v₁ = 1.334 x 10⁻¹¹ m/s
v₂ = u₂ + 2a₂d
v₂ = (0) + 2(6.67 x 10⁻¹³)(5)
v₂ = 6.67 x 10⁻¹² m/s
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I need help finding the kinetic energies (reupload)
Answer:
18.51 J
Explanation:
First, we need to find the Kinetic energy of the disk. Since the disk travels in a straight line, we can use the formula [tex]K=\frac{1}{2}mv^2[/tex]:
[tex]Kdisk=\frac{1}{2} 0.033*33.5^2\\Kdisk=18.51 J[/tex]
Since no other force is present, no friction, sound, or vibration, energy must be conserved. Therefore, the answer for both is 18.51 J.
If it takes 16.7 seconds for a wave to pass by and it has a wavelength of 13.8 meters, what is the speed of the wave to the nearest
Answer:
0.826
1 S.f.
0.8 m/s
Explanation:
S (speed) = D (Distance) / T (Time)
What is the moment of inertia (in units of gcm2) of an aluminum disk of radius 8.7 cm and thickness 3.0 mm spinning around its symmetry axis
For an aluminum disk of radius 8.7 cm and thickness 3.0 mm spinning around, moment of inertia is mathematically given as
I=16268.20gcm^2
What is the moment of inertia?Generally, the equation for the volume is mathematically given as
v=\pir^2t
Therefore
v=\pi(8.7)^2*0.32
v=76.09cm^3
In conclusion, The inertia
I=136.83*8.7^2/2
I=16268.20gcm^2
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A 208-volt, 4-wire, 3-phase wye power system feeds a school building. Daily voltage readings taken for 1 week are 205.25 volts, 203.75 volts, 208 volts, 204.35 volts, 206.7 volts, 207 volts, and 208.55 volts. What is the average daily voltage of the system
For a 208-volt, 4-wire, 3-phase wye power system feeds a school building, the average daily voltage is mathematically given as
x=206.23v
What is the average daily voltage of the system?Generally, the equation for the mean is mathematically given as
x=total sum/ number
Therefore
ts=05.25 volts, 203.75 volts, 208 volts, 204.35 volts, 206.7 volts, 207 volts, and 208.55 volts.
ts=1433.6
In conclusion
x=1433.6/7
x=206.23v
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25. Fossil fuels are carbon-containing deposits that form deep beneath
Earth's surface. Diana wants to show carbon moving to a location to form
fossil fuels. Which model most accurately shows this process?
A. She bubbles gas through a water sample.
B. She blows bubbles into the air and watches them spread.
C. She sprinkles breadcrumbs onto water and watches them sink.
D. She makes a replica of a volcano and shows magma erupting from it.
Answer:
B
Explanation: Carbon is released into the air by dead organisms, animals, and humans.
Question 3 of 20 :
Select the best answer for the question.
3. Which type of mental function would be the strongest and most obvious?
O A. Feeling
O B. Judging
O C. Introversion
O D. Observant
ما
Mark for review (Will be highlighted on the review page)
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The type of mental function that is the strongest and most obvious is feeling. That is option A.
Types of mental functionMental function can be defined as those activities that are performed by individuals such as thinking, sensing, or reasoning that involves the cognitive use of the brain.
The four basic cognitive functions include:
thinking, feeling, intuition, and sensation.The magnitude of each basic cognitive functions depends on the personality of the individual.
An extrovert is an individual that is active, outgoing, and has an expressive pattern of behaviour. Therefore extrovert feeling would be the strongest and most obvious.
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Help me please!!????
A current loop with radius 20 cm and current 2 A is in a uniform magnetic field of 0.5 T. Considering all possible orientations of the loop relative to the field, what is the largest potential energy difference (in Joules) you can find between two orientations
For a current loop with a radius 20 cm and current 2 A is in a uniform magnetic field of 0.5 T, largest potential energy difference is mathematically given as
du=0.2512J
What is the largest potential energy difference (in Joules) you can find between two orientations?Generally, the equation for the initial velocity is mathematically given as
v0=-iAB
Therefore
-2*\pi(0.2)(0.5))
v0=-0.1256J
for 180
theta=0180=-iABcos180
V180=0.1256J
Therefore
du=v180-v0
0.1258-(-0.1256
du=0.2512J
In conclusion, potential energy
du=0.2512J
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Which statement best describes a primary source?
Answer:
a first-hand or contemporary account of an event or topic.
Explanation:
The diagram shows a handle with three forces, each 100 N, applied to it. The handle is free to
move.
100N
100N
100N
handle
pivot
What is the effect of the forces on the handle?
A The handle will move downwards.
B The handle will not move.
с The handle will turn anticlockwise (to the left).
D The handle will turn clockwise (to the right).
Answer:
с The handle will turn anticlockwise (to the left).
Explanation:
8 Describe Explain how this transfer observes
the conservation of charge.
Charge is neither generated nor destroyed, according to the rule of conservation of charge. Charge is merely transferred from one item to another in the form of electrons.
4) A light beam shines through a thin slit and illuminates a distant screen. The central bright fringe on the screen is 1.00 cm wide, as measured between the dark fringes that border it on either side. Which of the following actions would decrease the width of the central bright fringe? (There may be more than one correct choice.) A) increase the wavelength of the light B) decrease the wavelength of the light C) increase the width of the slit D) decrease the width of the slit E) put the apparatus all under water
The actions that would decrease the width of the central bright are decrease in the wavelength of the light and Increase in the width of the slit.
Wavelength of the lightThe wavelength of the light is determined using the following formulas;
[tex]\lambda = d(\frac{y}{D} )[/tex]
where;
λ is wavelengthd is width of the slitD is the distance of the screeny is distance between the central bright fringe and dark fringeActions that would decrease the width of the central brighty = (λD) / (d)
Decrease in the wavelength of the lightIncrease in the width of the slitThus, the actions that would decrease the width of the central bright are decrease in the wavelength of the light and Increase in the width of the slit.
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Bodies weighing 2 and 6 kg acquired accelerations as a result of the interaction. Which body accelerates more and how many times?
Answer:
See below ~
Explanation:
Assume the bodies have the same acceleration
Equate each equation using the force formulaF = ma ⇒ F = 2aF = ma ⇒ F = 6aDivide the RHS of equation 2 by equation 1.
6a/2a3 timesTherefore, the body of 6 kg accelerates more by 3 times
A block oscillating on a spring has an amplitude of 20 cmcm. Part A Part complete What will the block's amplitude be if its total energy is doubled
Hi there!
Recall that the amplitude of an oscillating system occurs at a point of maximum potential energy.
For a spring system, potential energy is given as:
[tex]U = \frac{1}{2}kx^2[/tex]
U = Potential Energy (J)
k = Spring constant (N/m)
x = amplitude (m)
We can rearrange the equation to solve for amplitude more easily.
[tex]U = \frac{1}{2}kx^2\\\\2U = kx^2\\\\x^2 = \frac{2U}{k}\\\\x = \sqrt{\frac{2U}{k}}[/tex]
If we double 'U':
[tex]x' = \sqrt{\frac{2(2U)}{k}} = \sqrt{2}*\sqrt{\frac{2U}{k}}\\\\x' = \sqrt{2} * x[/tex]
Thus, the new amplitude would be √2 times greater, so:
[tex]20 cm \cdot \sqrt{2} = \boxed{28.284 cm}[/tex]
04*. The resultant of two force vectors A and B has a magnitude of 150 N along the y-axis. If the force vector B makes an angle of 60° with the positive x-axis, find the magnitude of B and the direction of A, given that the x-component of A is equal to -60 N. [120N, 142.48°)
(a) The magnitude of force vector B at the given resultant force is 120 N.
(b) The direction of force vector A is 142.46°
Resultant of the forcesThe resultant forces is calculated as follows;
Acosθ + Bcosθ = 0 --- (1)
Asinθ + Bsinθ = 150 ---- (2)
Magnitude of BAcosθ + Bcos60 = 0
-60 + Bsin60 = 0 (Acosθ = x-component of A = Ax)
Bcos60 = 60
B = 60/cos(60)
B = 120 N
Direction of AAsinθ + Bsinθ = 150
Ay + Bsinθ = 150
Ay + 120sin60 = 150
Ay = 150 - 120sin60
Ay = 46.1 N
[tex]tan \theta = \frac{A_y}{A_x} \\\\\theta = tan^{-1} (\frac{A_y}{A_x})\\\\\theta = tan^{-1} (\frac{46.1}{-60})\\\\\theta = -37.53^0\\\\\theta = -37.53^0 + 180 = 142.46^0[/tex]
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19. In a 16 Personalities Test, which
factor is opposite of judging?
O A. Prospecting
B. Turbulent
C. Intuition
O D. Feeling
Personality test is aimed at being able to decipher the nature of human personality. The opposite of judging in a personality test is prospecting.
What is a personality test?The term personality test is aimed at being able to decipher the nature of human personality through a Personalities Test.
In this personality test different personality types have their respective opposites. The opposite of judging in a personality test is prospecting.
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Answer:
prospecting
Explanation:
15. Which is a characteristic of a
judging approach?
O A. Liking things settled and organized
O B. Giving praise to others
C. Missing job opportunities
O D. Approaching work as play
According to Myers-Briggs, a charcteristic that is common to judging is liking things settled and organized.
What is judging?The term judging has to do with the quest for order and organization. It is one of the personality traits as outlined by Myers-Briggs.
The characteristic that is common among the people that exhibit the judging personality trait is liking things settled and organized.
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Answer:likes to have things settled and organized
Explanation:
bc I just took the test so ik it’s right
derive the equation of motion v²- u²= 2as
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Here we go ~
Let's use the given expression :
[tex]\qquad \tt \dashrightarrow \:a = v \dfrac{dv}{ds} [/tex]
[tex]\qquad \tt \dashrightarrow \:v \:dv= a \: {}{ds} [/tex]
Now, integrate both sides
[tex]\qquad \tt \dashrightarrow \: \int_{u}^v (v )\: dv= {\int _{0 }^{s} }{}^{} (a) \: {}{ds} [/tex]
[tex]\qquad \tt \dashrightarrow \: {\bigg[\dfrac{v {}^{2} }{2} \bigg]}_{u }^{v} \: = {\bigg[{a{s}^{} }{} \bigg]}_{0}^{s}[/tex]
[tex]\qquad \tt \dashrightarrow \: \dfrac{1}{2} {\bigg[{v {}^{2} - {u}^{2} }{} \bigg]}_{}^{} \: = a{\bigg[{{s - 0}^{} }{} \bigg]}_{}^{}[/tex]
[tex]\qquad \tt \dashrightarrow \: v {}^{2} - {u}^{2} =2 as[/tex]
[tex]\qquad \tt \: \therefore v {}^{2} =u {}^{2} + 2as[/tex]
I hope you understood ~