Answer:
a) The initial speed of the projectile is approximately 42.410 meters per second.
b) The speed of the projectile after 4 seconds is approximately 21.352 meters per second.
c) The horizontal range of the projectile is 169.64 meters.
d) The maximum height of the projectile is 68.775 meters.
e) The speed of the projectile when it landed on the ground is approximately 46.807 meters per second.
Explanation:
According to the statement, the projects shows a parabolic motion, which consists in the combination of horizontal uniform motion and vertical uniformly accelerated motion due to gravity. This motion is represented by the following equations of motion:
[tex]x = x_{o} + v_{o}\cdot t\cdot \cos \theta[/tex] (1)
[tex]y = y_{o} + v_{o}\cdot t\cdot \sin \theta + \frac{1}{2}\cdot g\cdot t^{2}[/tex] (2)
Where:
[tex]x_{o}[/tex], [tex]x[/tex] - Initial and current horizontal position, measured in meters.
[tex]y_{o}[/tex], [tex]y[/tex] - Initial and current vertical position, measured in meters.
[tex]\theta[/tex] - Launch angle, measured in sexagesimal angle.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]t[/tex] - Time, measured in second.
a) By using (2) and knowing that [tex]y_{o} = 20\,m[/tex], [tex]y = 0\,m[/tex], [tex]t = 8\,s[/tex], [tex]\theta = 60^{\circ}[/tex] and [tex]g = -9.807\,\frac{m}{s^{2}}[/tex], then initial speed of the projectile is:
[tex]v_{o}\cdot t \cdot \sin \theta = y-y_{o}-\frac{1}{2}\cdot g\cdot t^{2}[/tex]
[tex]v_{o} = \frac{y-y_{o}-\frac{1}{2}\cdot g\cdot t^{2} }{t\cdot \sin \theta}[/tex]
[tex]v_{o} = \frac{0\,m-20\,m-\frac{1}{2}\cdot \left(-9.807\,\frac{m}{s^{2}} \right)\cdot (8\,s)^{2} }{(8\,s)\cdot \sin 60^{\circ}}[/tex]
[tex]v_{o} \approx 42.410\,\frac{m}{s}[/tex]
The initial speed of the projectile is approximately 42.410 meters per second.
b) The vertical component of the velocity of the projectile is determine by differentiating (2) in time and substitute all known values:
[tex]v_{y} = v_{o}\cdot \sin \theta +g\cdot t[/tex] (3)
([tex]v_{o} \approx 42.410\,\frac{m}{s}[/tex], [tex]\theta = 60^{\circ}[/tex], [tex]g = -9.807\,\frac{m}{s^{2}}[/tex] and [tex]t = 4\,s[/tex])
[tex]v_{y} = -2.5\,\frac{m}{s}[/tex]
The horizontal component of the velocity of the projectile is:
[tex]v_{x} = v_{o}\cdot \cos \theta[/tex]
[tex]v_{x} = 21.205\,\frac{m}{s}[/tex]
And the speed of the projectile is determined by Pythagorean Theorem:
[tex]v = \sqrt{v_{x}^{2}+v_{y}^{2}}[/tex]
[tex]v = \sqrt{\left(21.205\,\frac{m}{s} \right)^{2}+\left(-2.5\,\frac{m}{s} \right)^{2}}[/tex]
[tex]v \approx 21.352\,\frac{m}{s}[/tex]
The speed of the projectile after 4 seconds is approximately 21.352 meters per second.
c) By (1) we find the horizontal range of the projectile:
([tex]x_{o} = 0\,m[/tex], [tex]v_{o} \approx 42.410\,\frac{m}{s}[/tex], [tex]\theta = 60^{\circ}[/tex], [tex]g = -9.807\,\frac{m}{s^{2}}[/tex] and [tex]t = 8\,s[/tex])
[tex]x = 0\,m + \left(42.410\,\frac{m}{s} \right)\cdot (8\,s)\cdot \cos 60^{\circ}[/tex]
[tex]x = 169.64\,m[/tex]
The horizontal range of the projectile is 169.64 meters.
d) The projectile reaches its maximum height when velocity is zero. By (3) and knowing that [tex]v_{y} = 0\,\frac{m}{s}[/tex], [tex]v_{o} \approx 42.410\,\frac{m}{s}[/tex] and [tex]g = -9.807\,\frac{m}{s^{2}}[/tex], the time associated with maximum height is:
[tex]0\,\frac{m}{s} = \left(42.410\,\frac{m}{s}\right)\cdot \sin 60^{\circ}+\left(-9.807\,\frac{m}{s^{2}} \right) \cdot t[/tex]
[tex]t = 3.745\,s[/tex]
And by (2) and knowing that [tex]y_{o} = 20\,m[/tex], [tex]v_{o} \approx 42.410\,\frac{m}{s}[/tex], [tex]t = 3.745\,s[/tex], [tex]\theta = 60^{\circ}[/tex] and [tex]g = -9.807\,\frac{m}{s^{2}}[/tex], the maximum height reached by the projectile is:
[tex]y = 20\,m + \left(42.410\,\frac{m}{s} \right)\cdot (3.745\,s)\cdot \sin 60^{\circ}+\frac{1}{2}\cdot \left(-9.807\,\frac{m}{s^{2}} \right)\cdot (3.745\,s)^{2}[/tex]
[tex]y = 68.775\,m[/tex]
The maximum height of the projectile is 68.775 meters.
e) If we know that [tex]y_{o} = 20\,m[/tex], [tex]v_{o} \approx 42.410\,\frac{m}{s}[/tex], [tex]t = 8\,s[/tex], [tex]\theta = 60^{\circ}[/tex] and [tex]g = -9.807\,\frac{m}{s^{2}}[/tex], the components of the speed are, respectively:
[tex]v_{y} = \left(42.410\,\frac{m}{s}\right)\cdot \sin 60^{\circ} + \left(-9.807\,\frac{m}{s^{2}} \right)\cdot (8\,s)[/tex]
[tex]v_{y} = -41.728\,\frac{m}{s}[/tex]
[tex]v_{x} = v_{o}\cdot \cos \theta[/tex]
[tex]v_{x} = 21.205\,\frac{m}{s}[/tex]
And the speed of the projectile is determined by Pythagorean Theorem:
[tex]v = \sqrt{v_{x}^{2}+v_{y}^{2}}[/tex]
[tex]v = \sqrt{\left(21.205\,\frac{m}{s} \right)^{2}+\left(-41.728\,\frac{m}{s} \right)^{2}}[/tex]
[tex]v \approx 46.807\,\frac{m}{s}[/tex]
The speed of the projectile when it landed on the ground is approximately 46.807 meters per second.
A building where it is very easy to hear soft voices is a acoustically dead room.
A. False
B. True
Answer:
False
Explanation:
i got it right
The statement is false. Because, the place where, it is easy to hear soft voices is acoustically good. Acoustically strong rooms facilitates the sound waves of even soft pitches.
What is Acoustics?Acoustics is the study of sound waves. Engineers strictly consider the concepts of acoustics to design the auditoriums and theater rooms to filter the sound effects in perfect pitches.
The frequency of a sound wave is called pitch. Thus lower frequency waves are lower pitch and they are termed as soft voices. Soft voices are hard to hear.
However, building where it is very easy to hear soft voices is acoustically good room. Therefore, the statement is false. The building is good in acoustics suitable for sound effects.
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A thermogram taken outside a house shows high amounts of thermal energy around the windows but not around the roof.
Which conclusion supports the thermogram?
The windows and the roof are energy efficient.
The windows and the roof are not energy efficient.
The windows are not energy efficient, but the roof is energy efficient.
The windows are energy efficient, but the roof is not energy efficient.
The conclusion supports the thermogram will be that the windows are not energy efficient, but the roof is energy efficient.
What is Thermography ?Thermography is a noninvasive method that employs an infrared camera to generate pictures that depict patterns of heat and blood flow on or near the body's surface.
A thermogram taken outside a house shows high amounts of thermal energy around the windows but not around the roof.
The conclusion supports the thermogram will be that the windows are not energy efficient, but the roof is energy efficient.
Hence option c is correct.
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If you dont want to read all of that it is option C
Find the volume and area of a spherical body of radius 49cm.
Explanation:
Area of sphere:4
[tex]4\pir {}^{2} [/tex]
4×3.14×49^2
=30156.56
volume of sphere:
[tex]4 \div 3pir {}^{3} [/tex]
4/3×3.14×49^3
492434.00
not sure
What is the squirrels escape velocity in mph if the squirrel accelerates at a constant 1.5 m/s squared from rest for 2.5s
Answer:
3.75 m/s
Explanation:
From the question given above, the following data were obtained:
Acceleration (a) = 1.5 m/s²
Initial velocity (u) = 0 m/s
Time (t) = 2.5 s
Final velocity (v) =?
a = (v – u) / t
1.5 = (v – 0) / 2.5
1.5 = v / 2.5
Cross multiply
v = 1.5 × 2.5
v = 3.75 m/s
Hence, the escape velocity of the squirrel is 3.75 m/s
Name two luminous objects other than the Sun
Answer:
The answer to this question is given below in this explanation section.
Explanation:
"Luminous objects"
Luminous object are objects that generate their own light. Illuminated objects are objects that are capable of reflecting light to our eyes.The sun is an example of a luminous objects,while the moon is an illuminated objects.During the day the sun generates sufficient light to illuminate objects on Earth.
Example:
The sunFlame in a lampTube lightElectric bulbName of luminous object
sun luminous moon luminousNon luminous object
Some object do not have their own light,they reflect light of other objects. These object are called non luminous object.
Example:
Moon reflect the light from the sun
other example are earth and other planets,paper,tree
-- any other star
-- a firefly
-- a flashlight
-- a meteor
-- a street light
-- a car headlight
-- a burning log
-- a night light
-- the hot wire in a toaster
-- an LED
-- a laser
-- a burning match
-- a lit candle
write a summary of Albert Einstein accomplishments
Answer:
He is also known for his discovery of the photoelectric effect, for which he won the Nobel Prize for Physics in 1921. Einstein developed a theory of special and general relativity, which helped to complicate and expand upon theories that had been put forth by Isaac Newton over 200 years prior.
answer :-He is also known for his discovery of the photoelectric effect, for which he won the Nobel Prize for Physics in 1921. Einstein developed a theory of special and general relativity, which helped to complicate and expand upon theories that had been put forth by Isaac Newton over 200 years prior.
When a force of 2.4 newtons is applied to a spring, the extension is 0.4 m. What is the spring constant?
6 N/m
9.6 N/m
2 N/m
2.4 N/m
Answer:
6N/m
Explanation:
k = Fe
f = 2.4
e = 0.4
2.4 ÷ 0.4
= 6N/m
___ is the rate of change of velocity of an object? Formula: ___
Answer:
Acceleration is the rate of change of velocity of an object.
Formula: Had to take a picture of the formula
Answer:
Acceleration is the rate of change of velocity of an object.
Formula:
[tex]a=\frac{v-v_{0} }{t}[/tex]
The formula is basically the change in velocity over the time
a is the acceleration
v is the final velocity
v0 is the starting/initial velocity
t is the time elapsed
Hope this helps :)
Who do you think the target market of these advertisements is? Explain.
Answer:
uhhhhhhh wait what
Explanation:
What advertisement
Why are drills performed in drum beats
Answer:
The drum drill is just one option in stride frequency development. Most of the time, the drum drill can be seen as just a rhythm drill that allows an athlete to relax and experiment with the right range of motion and bounce. A solid background in floating drills and developing reactivity should help athletes mold their stride into a balanced motion that maximizes their speed.
I have used frequency drills for years and now understand the nature of stride development mainly from shaping the stride parameters we all have known about for a long time. The drum drill is a special exercise that can make a great change in athletes who are receptive to improving and with a coach who is worth their salt in instruction. The drum drill is just one option for improving an athlete, and it’s more than fine to use any method you see fit that helps improve stride frequency.
Explanation:
Explanation:
Most of the time, the drum drill can be seen as just a rhythm drill that allows an athlete to relax and experiment with the right range of motion and bounce. A solid background in floating drills and developing reactivity should help athletes mold their stride into a balanced motion that maximizes their speed
We break down a UK drill beat, a genre that rapidly became one of the ... Beat Dissected is a regular series in which we deconstruct drum patterns, ... an 808 bass line with plenty of glides and a piano played back in halftime.
give two differences between mass and weight
Answer: 1) Mass is a scalar quantity while weight is a vector quantity
2) Mass is measured in Gramma and kilogram while weight is measured in Newton.
Explanation:
Mass can be defined as the amount of matter that comprises an object. It is a scalar quantity, that is, it has magnitude. It is measured in kilogram with its unit in Kg. Mass is measured using an ordinary weighing scale.
Weight can be defined as the force acted upon an object due to gravity. Weight is a vector quantity, that is, it has both magnitude and direction towards the center of the earth. Weight can be measured with the use of a spring balance. Its unit is in Newton.
Okay I need help with this question.....-_-
When does an object have no kinetic energy
P.S I need the answer ASAP
Answer:
A
Explanation:
an object has no kinetic energy when its at rest
can someone please explain some calculations on vernier calliper
Answer:
Hey mate here's your answer ⤵️
Vernier caliper least counts formula is calculated by dividing the smallest reading of the main scale with the total number of divisions of the vernier scale.LC of vernier caliper is the difference between one smallest reading of the main scale and one smallest reading of vernier scale which is 0.1 mm 0r 0.01 cm
Hope it was helpfulllWhich element would Element X most likely be grouped with on the periodic table?
Answer:
group 0
Explanation:
it might be xenon (Xe)
According to the electronic configuration, and assuming the element to be halogen it is most likely to be grouped with potassium as halogens are in need of one electron which is easily made available by potassium.
What is electronic configuration ?Electronic configuration is defined as the distribution of electrons which are present in an atom or molecule in atomic or molecular orbitals.It describes how each electron moves independently in an orbital.
Knowledge of electronic configuration is necessary for understanding the structure of periodic table.It helps in understanding the chemical properties of elements.
Elements undergo chemical reactions in order to achieve stability. Main group elements obey the octet rule in their electronic configuration while the transition elements follow the 18 electron rule. Noble elements have valence shell complete in ground state and hence are said to be stable.
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what is the dimensional consistency of s = Vot + 1/2 at2
Answer:
The formula is dimensionally consistent
Explanation:
Dimensional Analysis
There are three fundamental magnitudes in Physics:
L = Length
T = Time
M = Mass
All the formulas and equations that use physical magnitudes must be consistent in their units.
For example, the formula:
[tex]\displaystyle s=v_ot+\frac{1}{2}at^2[/tex]
Is used to calculate the distance traveled by an object, knowing its initial speed vo, acceleration a, and time t.
The units for each magnitude are:
s = L
vo = L/T or [tex]LT^{-1}[/tex]
a = L/T^2 or [tex]LT^{-2}[/tex]
Let's analyze the dimensions of the magnitudes in the formula (the constant 1/2 is neglected because it doesn't affect the dimensional analysis):
[tex]\displaystyle L=L/T*T+L/T^2*T^2[/tex]
The first term simplifies to L because the T's simplify. The same happens with the second term, the squared T's simplify:
[tex]\displaystyle L=L+L[/tex]
Thus the formula is dimensionally consistent
Katie is walking in an orange grove. She looks at all of the orange trees. She wants to find out how many seeds are in each orange.
What can she do to collect data?
A.
Measure each tree to see how tall it is.
B.
Gather a few oranges and see how many seeds are in each.
C.
Plant an orange seed and see how much fruit grows on the tree.
D.
Count the number of trees in the grove.
Answer:
What she can do to collect the data is;
B. Gather a few oranges and see how many seeds are in each
Explanation:
The quantity Katie wants to find out is the number of seeds contained in each orange
Therefore, the required population = The number of seeds in a given orange
The method of estimation of the number of seeds per orange is sampling method, whereby the number of seeds in each of the orange in the sample is used to as an hypothesis as to the number of seeds expected in each orange of the entire population.
Therefore, in order to collect the data, she can gather a few oranges and see how many seeds are in each.
If a moving body of mass 100g has kinetic energy 45 joules, what will be it's velocity?
Answer:
[tex]\boxed{\pink{\sf Velocity \ of \ the \ body \ is \ 30m/s .}}[/tex]
Explanation:
Given that a body is moving which has a mass of 100g. And its Kinetic energy is 45 Joules . We need to find its velocity . So ,
[tex]\boxed{\red{\bf Kinetic\: Energy =\dfrac{1}{2}mv^2 }}[/tex]
Now here mass is in grams. So converting it into SI units we have , 100/1000 kg = 0.1 kg
[tex]\implies KE =\dfrac{1}{2}mv^2 \\\\\implies 45 J = \dfrac{1}{2}\times \dfrac{1}{10} kg \times v^2 \\\\\implies v^2 = 45 \times 20 \\\\\implies v^2 = 900 m^2/s^2 \\\\\implies v =\sqrt{900 m^2/s^2} \\\\\underline{\boxed{\blue{\tt \implies Velocity = 30m/s }}}[/tex]
A bus starts to move from rest. If it is accelerated by 0.8m/s2, calculate the velocity and distance traveled after 8 s.
We are given:_______________________________________________
Initial velocity (u) = 0 m/s
acceleration (a) = 0.8 m/s²
time interval (t) = 8 seconds
final velocity (v) = v m/s
distance travelled (s) = s m
Solving for the final velocity:___________________________________
We know that:
v = u + at [first equation of motion]
v = 0 + (0.8)(8) [replacing the variables]
v = 6.4 m/s
Hence, the final velocity is 6.4 m/s
Solving for the distance travelled:_______________________________
We know that:
s = ut + 1/2(at²) [second equation of motion]
s = (0)(8) + 1/2(0.8)(8)(8) [replacing the variables]
s = 1/2(6.4*8)
s = 25.6 m
Hence, the distance travelled is 25.6 m
The figure below shows a 2 kg box. A 10 N force pushes the box horizontally across a level flat surface. The frictional force that results from contact with the surface produces a 2 N force that opposes the direction of the box's movement. image What is the net force acting on the box?
A. 5 N, right
B. 8 N, right
C. 20 N, right
D. 12 N, right
Fricition opposes the pushing force, so the net force is
10 N - 2 N = 8 N
to the right.
The dancing bear family loves when their trainer gives them little treats to reward them for a good performance. If the trainer gives the dancing bear family 34 treats each show, how many treats will the trainer need for 22 shows?
Answer:
748 treats.
Explanation:
If the trainer gives out 34 treats and gave them out for 22 shows, then to find the total you need to multiply 34 by 22, or (a longer but more simple way) add 34, 22 times.
If you had a cup of hot tea, will the tea generally stop cooling when it reaches room temperature? Or will it keep cooling further (in small increments)?
Answer:
The tea will generally stop cooling when it reaches room temperature ️
A student of 4 feet tall went for swimming in a pool. He saw the depth of water in the pole less than 4 feet .Will he sink , write with reason
Answer:
he will not be drowned
Explanation:
Question says , the height of the student = 4 feet,
Depth of the pool( in feet ) be x ( say ) which is less than 4 feet,
Clearly, the depth of the pool < height of the student,
This means, if the student goes for swimming in the pool, however he does not know swimming, he will not be drowned until he is suffering from an injury or external force.
Distinguish between heat and work in terms of energy
Answer:
Heat is the energy associated with the random motion of particles, while work is the energy of ordered motion in one direction. Therefore heat is "low-quality" energy and work is "high-quality" energy, and this supports the entropy statement of the Second Law.
Explanation:
1. A truck with a mass of 8, 000 kg is traveling at 26.8 m/s when it hits the brakes. A.)What is the momentum of the truck before it hits the brakes?
B.)The truck comes to a stop, losing all of that momentum. It takes 12.4 s for the truck to come to a
complete stop. How much force does it take to stop the truck?
Answer:
1. A.) The moment of the truck before it hits the brakes is 214,400 kg·m/s
B.) The force it takes to stop the truck is approximately 17,290.4 N
Explanation:
1. A.) The given parameters are;
The mass of the truck, m = 8,000 kg
The velocity of the truck when it hits the brakes, u = 26.8 m/s
Momentum = Mass × Velocity
The moment of the truck = The mass of the truck × The velocity of the truck
Therefore;
The moment of the truck before it hits the brakes = 8,000 kg × 26.8 m/s = 214,400 kg·m/s
B.) The amount of momentum lost when the truck comes to a stop = The initial momentum of the truck
The time it takes the truck to come to a complete stop, t = 12.4 s
The deceleration, "a" of the truck is given by the following kinematic equation of motion
v = u - a·t
Where;
v = The final velocity of the truck = 0 m/s
u = The initial velocity = 26.8 m/s
a = the deceleration of the truck
t = The time of deceleration of the truck = 12.4 s
Substituting the known values gives;
0 = 26.8 - a × 12.4
Therefore;
26.8 = a × 12.4
a = 26.8/12.4 ≈ 2.1613
The deceleration (negative acceleration) of the truck, a ≈ 2.1613 m/s²
Force = Mass × Acceleration
The force required to stop the truck = The mass pf the truck × The deceleration (negative acceleration) given to the truck
∴ The force it takes to stop the truck = 8,000 kg × 2.1613 m/s² ≈ 17,290.4 N.
1 A student says that current is the amount of charge. Is he correct? Explain your answer.
Answer:
No he's not correct. Current is the rate of flow of charge. 1 Ampere is the amount of 1 coulomb of charge that flows per second. 10 Ampere would then be 10 coulomb of charge flowing in one second.
The frictional force exerted by the road on the body is
Answer:
Explanation:
Frictional force can be defined as the force that is generated by two surfaces which are in contact with each other and even goes ahead to slide against each other. It can also be simply defined as a force that oppose the sliding of one object over the other
There are different types of frictional forces such as dry friction, lubricated friction, internal friction, fluid friction etc. One of the factors that affects frictional forces is that the forces are majorly affected by the surface texture and amount of force that bounds them together.
Madeline fires a bullet horizontally. The rifle is 1.9 meters above the ground. The bullet travels 200 meters horizontally before it hits the ground. What speed did Madeline's bullet have when it exited the rifle?
Answer:
322.6 m/s
Explanation:
Given that there are two components of position;
x= vot
y component is;
y= 1.9 - gt^2/2
When the bullet hits the ground, y=0
1.9 -gt^2/2 =0
Where g = 10ms^-2
t= √2 × 1.9/10
t= 0.62 secs
Therefore,
x= vot
vo = x/t
Where, x= 200 m
vo= 200/0.62 =
vo= 322.6 m/s
What happens in synthesis
Answer:
S phase or Synthesis
Explanation:
Is the phase of the cell cycle when DNA packaged into chromosomes is replicated. This even is an essential aspect of the cell cycle because replication allows for each cell created by cell division to have the same genetic make-up.
Hope this helps!!
- Which of the following does not move as a transverse wave?
A ultraviolet light
B sound wave
C surface water wave
D microwave
Which of these effects describes the change in pitch we hear
moving motorbike goes past?
A total internal reflection
B.refraction
C reflection
D Doppler
Which of the following does not make use of total internal re
A oscilloscope
B endoscope
C prismatic periscope
D optical fibres
Help me
will give the brainliest!
Please answer correctly.
Answer:
- Which of the following does not move as a transverse wave?
B. sound waves
because sound waves are longitudinal waves having compressions and rare factions.
Which of these effects describes the change in pitch we hear
moving motorbike goes past?
D. Doppler effect
Doppler effect is the phenomenon where there is apparent change in frequency (pitch) and wavelength of a wave due to relative motion of the sound source.
Which of the following does not make use of total internal reflection.
B. Endoscope
Endoscope doesn't use total internal reflection since no refraction takes place.
The teacher has 12 green and 15 purple stickers the students are given `an equal number of each color stickers how many green and purple stickers does each students get
Answer:
Each student gets 4 green stickers and 5 purple stickers or a total of 9 stickers.
Explanation:
The greatest common divisor (GCD) of two or more natural numbers or integers (not numbers with decimals) is the largest number that divides them. In other words, the Greatest Common Divisor is the greatest of the common divisors of several numbers. To calculate it, each of them is decomposed into prime factors. The GCD is the result of multiplying the factors that are repeated in all the decompositions, affected by the smallest exponent.
In the event that no factor is repeated, the GCD of those numbers is 1, and the numbers are said to be "prime to each other."
In this case, the decomposition of 12 and 15 is:
12 = 2²*3.
15=3*5
So the GCD between 12 and 15 is 3
Now, to calculate how many green and purple stickers each student receives, you simply divide the amount of each sticker color by 3.
12÷3= 4
15÷3= 5
So, each student gets 4 green stickers and 5 purple stickers or a total of 9 stickers.