Against the park ranger's advice, a visitor at a national park throws a stone horizontally off the edge of a 83 m high cliff and it lands a distance of 93 m from the edge of the cliff, narrowly missing a visitor below.
What was the initial horizontal velocity of the rock, in m/s? You can round your answer to the hundredths place and use g ≈ 10 m/s2.
Answer:
20.37m/s
Explanation:
For this problem, we'll need a basic kinematic equation for both directions
Vertical direction:
\(y(t)=\frac{1}{2}a_{y}t^{2}+v_{o_y}t+y_{o}\)
Knowing that the acceleration in the y-direction is due to gravity, and is constant near the surface of the Earth, where the rock is being thrown, we get \(a_{y}=g=-10m/s^{2}\). We're also given that the initial vertical height is 83m, so \(y_o=83m\). Additionally, we're given that the stone is thrown horizontally, and thus initially, it has no vertical velocity. Only velocity in the x-direction. Thus, \(v_{o_y}=0m/s\). Substituting known values into our equation:
\(y(t)=\frac{1}{2}(-10)t^{2}+(0)t+(83)\)
\(y(t)=-5t^{2}+83\)
This equation is true for all times until the acceleration changes (isn't constant... i.e. when it hits the ground).
What now?
We want to find the specific time when it does hit the ground. Why? Because this is the point in time where we know some extra information about what is happening in the x direction, and that will help us deal with the x-direction equation.
When the stone does hit the ground, the output of this function (measuring the height of the stone) is zero, which leaves only one unknown value, t... the time associated with that y: the time that it takes to hit the ground:
\(0=-5(t_{ground})^{2}+83\\-83=-5(t_{ground})^{2}\\\frac{-83}{-5}=(t_{ground})^{2}\\16.6=(t_{ground})^{2}\\\sqrt{16.6}=\sqrt{(t_{ground})^2}\\4.074309757seconds=t_{ground}\)
Again, this is the time that the stone hits the ground. Knowing how special this time is, one might give it a special subscript to keep track of it.
\(t_{ground}=4.074309757seconds\)
Horizontal direction
Reusing the basic kinematic equation for the horizontal direction:
\(x(t)=\frac{1}{2}a_{x}t^{2}+v_{o_x}t+x_{o}\)
Note that in the horizontal direction, there is no acceleration (after the rock is released), so \(a_{x}=0\). Also, if we define the base of the cliff as our origin, then at the top of the cliff where the rock is released, the initial x-position is still zero, aka, \(x_{o}=0\)
\(x(t)=\frac{1}{2}(0)t^{2}+v_{o_x}t+(0)\\x(t)=v_{o_x}t\)
While we don't know the initial horizontal velocity, we do know an output of the function for one specific input... we know that when the stone hits the ground, that the stone's horizontal distance is 93m from the cliff. So, if we input \(t_{ground}\) into this function, it will give an output of 93. The only remaining unknown is the initial velocity in the x direction. One equation, one unknown, we can solve this:
\(x(t_{ground})=v_{o_x}t_{ground}\\83=v_{o_x}(4.074309757)\\\frac{83}{4.074309757} =v_{o_x}\\20.37154879m/s =v_{o_x}\\\)
If there were a component of initial velocity in the y direction, we would need to use the Pythagorean theorem to combine them. However, as the initial y component of velocity is zero, the initial velocity is simply the initial x velocity.
Paying attention to directions, round to the answer to the nearest hundredth:
\(20.37m/s =v_{o}\\\)
why can an observable interference pattern never be obtained between two monochromatic beams of light
An observable interference pattern can never be obtained between two monochromatic beams of light because they have a fixed phase relationship and no relative phase shift, resulting in a constant intensity pattern.
In order to observe an interference pattern, two or more waves must meet and interfere with each other. This interference can be constructive, where the waves add together to create a larger amplitude, or destructive, where the waves cancel each other out. However, two monochromatic beams of light have a fixed frequency and a fixed phase relationship, which means that they will always interfere in the same way, with no variation in phase or amplitude. As a result, they will produce a constant intensity pattern rather than an observable interference pattern. To create an interference pattern, multiple light sources with varying phases and amplitudes are required.
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Today's nanotechnology-produced computer transistors are roughly equivalent in size to
A) the width of a fingernail.
B) a human hair.
C) a virus.
D) an atom.
B) A human hair. Today's nanotechnology-produced computer transistors are roughly equivalent in size to a human hair.
Transistors are electronic devices that are used to amplify or switch electronic signals and electrical power. They are fundamental building blocks of modern electronic devices and integrated circuits. Transistors are typically made from semiconductor materials, such as silicon, and they consist of three layers: the emitter, base, and collector. The size of transistors has been continuously shrinking over the years due to advancements in nanotechnology, allowing for more transistors to be packed onto a single chip, resulting in increased computational power and miniaturization of electronic devices. Today, transistors can be manufactured at the nanoscale, with dimensions on the order of tens of nanometers or even smaller.
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what is the horizontal distance dforearm between the elbow and the point where the weight of the forearm acts?
The horizontal distance (d_forearm) between the elbow and the point where the weight of the forearm acts is known as the center of mass of the forearm.
The center of mass represents the average position of the weight distribution of an object. In the case of the forearm, this point is important in biomechanics as it helps determine the force exerted by the muscles and the stability of the arm during various movements. To find the center of mass, one can use various techniques including mathematical calculations, experimental measurements, and observation of the anatomy.
Generally, the center of mass for the human forearm is located approximately at the midpoint between the elbow and the wrist, making it roughly 50% of the total length of the forearm. However, this location may vary among individuals due to differences in body proportions, muscle mass, and bone density. In summary, the horizontal distance (d_forearm) between the elbow and the point where the weight of the forearm acts is the center of mass, typically located around the midpoint of the forearm, this point plays a significant role in the biomechanics and stability of the arm during various movements.
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which statement is true about electron shielding of nuclear charge?
Electron shielding reduces the effective nuclear charge.
Does electron shielding decrease the effective nuclear charge?Electron shielding refers to the phenomenon where inner electron shells in an atom partially block the attractive force of the positively charged nucleus on the outer electrons. This shielding effect arises from the repulsion between negatively charged electrons. As a result, the outer electrons experience a reduced effective nuclear charge, which is the positive charge felt by an electron due to the nucleus.
The shielding effect can be explained by considering the electron distribution in an atom. Inner electrons occupy regions closer to the nucleus, creating a barrier that diminishes the electrostatic attraction between the outer electrons and the nucleus. This reduction in the effective nuclear charge affects various atomic properties, such as atomic size and ionization energy.
the concept of electron shielding and its impact on atomic properties, including atomic radius and ionization energy. Understanding electron shielding helps in explaining trends and behaviors observed in the periodic table.
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A steel wire 4.5 m long stretches 0.15 cm when it is given a tension of 370 N. What is the diameter of the wire?
A steel wire 4.5 m long stretches 0.15 cm when it is given a tension of 370 N. then the diameter of the wire is 2.6 × 10⁻³ m.
Given,
length of the wire L = 4.5 m
elongation l = 0.15 cm = 0.15 × 10⁻² m
restoring force F = 370 N
In this problem young's modulus of the wire is not given, consider the young's modulus of the wire is Y = 2 × 10¹¹ pa.
Youngs modulus Y = Fl ÷ AL
where A is cross sectional area of the wire,
Putting all the values
2 × 10¹¹ pa. = 370 N × 4.5 m ÷ A × 0.15 × 10⁻² m
A. = 370 N × 4.5 m ÷ 2 × 10¹¹ pa × 0.15 × 10⁻² m
A = 5.55 × 10⁻⁶
πr² = 5.55 × 10⁻⁶
r = 1.32 × 10⁻³ m
Diameter d = 2r = 2 × 1.32 × 10⁻³ m = 2.6 × 10⁻³ m.
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When a system fails it _____ our other systems causing us to be sick.
A. connects
B. repairs
C. affects
D. structures
Answer:
c) affects
Explanation:
im like 90% sure
A projectile is fired vertically upward with an initial velocity of 190 m/s. Find the maximum height of the projectile
ANSWER
\(1841.84\text{ m}\)EXPLANATION
Parameteters given:
Initial velocity = 190 m/s
To find the maximum height, we apply the formula for the maximum height of a projectile:
\(H=\frac{u^2\sin ^2\theta}{2g}\)where u = initial velocity
θ = angle with the horizontal
g = acceleration due to gravity = 9.8 m/s²
From the question, the projectile is fired vertically upward. This means that the projectile will make a 90° angle with the horizontal.
Therefore, we have that the maximum height of the projectile is:
\(\begin{gathered} H=\frac{190^2\cdot\sin ^2(90)}{2\cdot9.8} \\ H=1841.84\text{ m} \end{gathered}\)Answer:
Height is equal to 1841.8367m
Explanation:
KE = GPE
Write out the formula
1/2(m)(v^2) = mgh
Fill it with the information you have
1/2(190^2) = (9.8)(h)
Solve
1/2(36100) = 9.8h
18050 = 9.8h
1841.83673 = h
Write the complete answer out
Maximum height is equal to 1841.8367m (meters)
A person lifts a 11.1 kg box of bricks a vertical distance of 1.40 m and then carries the box horizontally a distance of 8.00 m. How much work is done by the person in the process?
Explanation:
Assuming that the person is the only force applying work to the box, the total work done by the person is 993.4 J. This is calculated by multiplying the force of gravity (98.1 N) with the vertical distance (1.40 m) to obtain 137.4 J, and then adding the work done in carrying the box horizontally (8.00 m × 98.1 N = 756.8 J). Therefore, the total work done is 137.4 J + 756.8 J = 993.4 J.
3.Minsoo is training for cross-country in the fall. He ran 5 miles east. Then he turned around and ran 4 miles west. Draw and label the vectors that show each segment of his trip and the resultant displacement vector. Find his resultant displacement. (10 points)
Answer:
...............................
If the earth had three times the radius but the same mass, how would this change the weight of the object?
Answer:
It will be 1/9 of its previous value
Explanation:
Weight = mass x gravity
Gravity = GM / r² (G is the constant)
Since the new radius is three times r, we plug in 3r:
New gravity = \(\frac{GM}{(3r)^{2} }\)
Since the new gravity is 1/9th of the original gravity, the new weight is 1/9th the original weight.
Could you please help me with this question
Calculate the current through the resistor in the circuit shown below.
Answer:
0.6amp or I= 0.6
Explanation:
V=IR
12V=I(20)
12/20=I
0.6=I
Answer:
0.6amp
Explanation:
Reset all. Set the force back to 1 N. 14. Hit start, wait about 2 seconds, and set the brake force to 1 N. Hit enter and observe. 15. Describe the motion of the wheel: ______________________________________ 16. What happened to the acceleration vector
In the given scenario, if the force is reset back to 1 N, hit start and then set the brake force to 1 N, and then hit enter, the motion of the wheel will either be zero (if the brake force is applied) or it will be in a state of constant velocity (if no brake force is applied).
In this scenario, the acceleration vector will be zero since there is no force acting on the object.
When a force acts on a body, it can cause it to either change its velocity or change its direction, or both.
If no force acts on the body, the object will remain in a state of rest or constant motion.
In the given scenario, if there is no force acting on the wheel, it will remain in a state of constant motion.
Therefore, the acceleration vector will be zero.
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Change the speed 6 m/s into km/hr
Answer:
For changing the speed from m/s to km/h we just have to multiply the number with
18
5
So,
Here speed given is 6 m/s
To convert it into km/h =
6
×
18
5
=
21.6
km/h
Hence the correct answer is 21.6 km/h
A physical property is a characteristic of a substance that can be observed or measured without changing the identity of the substance. Physical properties include color, density, hardness, and melting and boiling points. A chemical property describes the ability of a substance to undergo a specific chemical change.
Answer:
True
Explanation:
The main differences between a physical property and a chemical property are mentioned below:
A physical property is a characteristic of a substance that can be observed or measured without changing the identity of the substance. Physical properties include color, density, hardness, and melting and boiling points.
While A chemical property describes the ability of a substance to undergo a specific chemical change.
¿Una bombilla de 50 vatios transfiere mas energía por unidad de tiempo que una bombilla de 100 vatios?
Does a 50-watt light bulb transfer more energy per unit of time than a 100-watt light bulb?
Answer:
yes it does transfer more energy per unit
Explain how the stars impact the shape of a galaxy.
Answer:
Galaxies are too far away for astronomers to take real 3D measurements, but we can infer their shape based on the movement of stars. ... This is also true of less common spiral galaxies like the Milky Way. The bulge near the center contains older stars, while the flattened arms are home to younger ones.
Explanation:
The orbits of stars can also affect the shape of a galaxy through a variety of density waves that are produced when material is compressed into something comparable to a traffic jam in galaxies.
What is Star?A star is defined as a celestial object consisting of a luminous sphere of plasma held together by self-gravity where the closest star to Earth is the Sun. While many other stars are visible to the uncovered eye at night, their extreme distance from Earth causes them to appear as fixed points of light.
Galaxies are too far away for astronomers to take true 3D measurements, through which we can estimate their size based on the motion of stars, which is also true for less common spiral galaxies like the Milky Way.
Thus, the orbits of stars can also affect the shape of a galaxy through a variety of density waves that are produced when material is compressed into something comparable to a traffic jam in galaxies.
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A string is being pulled with a force of 20 N and moves a 5 kg block to the left at a constant speed. What is the coefficient of friction for between the floor and the block? Enter your answer as a decimal value (Example: 0.72) * I think the answer is 20 but this question is starting frustrating me
Answer:
μ = 0.4
Explanation:
As, the object is moving at a constant speed. Therefore, the unbalanced force on it must be equal to zero. So, the frictional force on the object must be equal to the force applied to it:
F = frictional force
F = μR = μW = μmg
where,
F = Applied Force = 20 N
μ = coefficient of friction between wall and floor = ?
m = mass of block = 5 kg
g = 9.8 m/s²
Therefore,
20 N = μ(5 kg)(9.8 m/s²)
μ = 20 N/49 N
μ = 0.4
Aaron walks 5 miles every day for exercise, leaving his front porch at 5:00 am. And returning to his porch at 6:00 am. What is the total displacement of his daily walk? *
need to know the answer now
Answer:
Total displacement = 0
Explanation:
He lives his front porch and still returns to his front porch.
Now, displacement is a vector quantity and as such, it is the distance between the initial point of movement and the final point of movement.
In this case the initial point is the same as the final point and thus the displacement is zero.
A man has a 90 kg mass on Earth. If the moon has 1/6 of the gravity as the earth,
what is the mass of a 90 kg man on the moon?
what are the five properties of light
Answer: I believe it's dispersion, diffraction, reflection of light, refraction of light, polarization of light and interference of light.
Explanation:
what is humidity???
Answer:
presence of moisture in air
Humidity is the amount of water vapor in the air.
hope it helps you!!!!!!!!
6. Sandy adds 3 sugar packets to her tea in order to make it sweeter. She stirs in the sugar and then takes a sip. She notices that not all the sugar was dissolved. What type of solution did she make?
A. Saturated B.Unsaturated C.Supersaturated D.Mildly saturated
Answer:
C.Supersaturated
Explanation:
There are three types of solution:
SATURATED SOLUTION:
It is the solution that contains maximum amount of solute dissolved in a solution in normal conditions.
UNSATURATED SOLUTION:
It is the solution that contains less than the maximum amount of solute dissolved in a solution in normal conditions. It has space for more solute to be dissolved in it.
SUPERSATURATED SOLUTION:
It contains more than the maximum amount of solute dissolved in it. Such a solution has no capacity to dissolve any more solute under any conditions.
Since the sugar is no more dissolving in the tea and has settled down. Therefore, the solution is:
C.Supersaturated
Be careful of the wire size application chart you use, because many of them allow up to a ____ voltage drop over the length of the wire, which is more than is allowed in most automotive circuits. Group of answer choices
Answer: 0.1
Explanation: The wire size is very important when making decisions on the wiring of any equipment,house and other things. It has also been found that the size of the wire determines the load that can be allowed through it.
The right wire size application chart should always be considered before selecting the wiring diagram or system for any building or equipment as it can help to determine the amount of voltage that can be effectively carried through it.
Kieran ran 8 laps of the track in 18 minutes. Jevon ran 6 laps of the track. Who had a greater average speed
Kieran had a greater average speed than Jevon. Let us go into more detail in the explanation below. To compare the average speeds of Kieran and Jevon, we need to find out the speed of each person.
We can use the formula speed = distance/time. Kieran ran 8 laps in 18 minutes, which means he ran 8/18 = 0.44 laps per minute. To find out Kieran's speed, we need to multiply this by the length of one lap. If we assume that the length of one lap is 400 meters, then Kieran's speed is:0.44 laps per minute × 400 meters per lap = 176 meters per minute Jevon ran 6 laps of the track, but we don't know how long it took him.
Therefore, we can't calculate his speed directly. However, we can still compare his speed to Kieran's by using ratios. If we assume that Jevon ran the same length of track as Kieran, then we can write the following equation: Kieran's speed/Jevon's speed = Jevon's time/Kieran's time.
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a) Calculate the magnitude of displacement of the car in 40 seconds. b) During which part of the journey was the car accelerating? c) Calculate the magnitude of average velocity of the car.
Answer:
a) 600 meters
b) between 0 and 10 seconds, and between 30 and 40 seconds.
c) the average of the magnitude of the velocity function is 15 m/s
Explanation:
a) In order to find the magnitude of the car's displacement in 40 seconds,we need to find the area under the curve (integral of the depicted velocity function) between 0 and 40 seconds. Since the area is that of a trapezoid, we can calculate it directly from geometry:
\(Area \,\,Trapezoid=(\left[B+b]\,(H/2)\\displacement= \left[(40-0)+(30-10)\right] \,(20/2)=600\,\,m\)
b) The car is accelerating when the velocity is changing, so we see that the velocity is changing (increasing) between 0 and 10 seconds, and we also see the velocity decreasing between 30 and 40 seconds.
Notice that between 10 and 30 seconds the velocity is constant (doesn't change) of magnitude 20 m/s, so in this section of the trip there is NO acceleration.
c) To calculate the average of a function that is changing over time, we do it through calculus, using the formula for average of a function:
\(Average\,of\,f(x)=\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx\)
Notice that the limits of integration for our case are 0 and 40 seconds, and that we have already calculated the area under the velocity function (the integral) in step a), so the average velocity becomes:
\(Avearage=\frac{600\,\,m}{40\,\,s}= 15\,\,\frac{m}s}\)
explore how archemides principle is applied in building a ship and submarine
Answer:
Principle Archimedes is applied in building a ship and submarine using the manipulating that buoyancy, is controlled the ballast tank system.
Explanation:
Submarine is rather had they focused on main parts of the submarine,he is complex and long process implementation,the most submarine design like submarine stability.
Submarine stability is complete and the fundamental Archimedes principle to arrive the weight of submarine is equal to buoyancy force.
Submarine into the parts and components of ballast tank the sequence in diving and surfacing,there two vital parts:- flood parts and air vents
flood parts:- at the bottom position and allow water to enter or leave that tank.
air vents:- air vents at the top of the pressure hall,and that they submarine dive.
this time submarine is most modern system is depth is 300 to 450 meters,high pressure air is 15 bar is tank air valve.
submarine is basic of the effective volume of all the submarine surfaced condition,submarine minus to the free water flood is equal to the fully pressure hull,submarine is the surfaced condition.
HURRY I NEED IT NOW What is the density at 20oC of 12.0 milliliters of a liquid that has a mass of 4.05 grams?
0.338 g/mL
2.96 g/mL
16.1 g/mL
48.6 g/mL
Density is the mass per unit volume of any object. It is calculated by dividing the mass of an object by its volume. This is:
ρ = m/V
ρ = 4.05 g / 12 mL
ρ = 0.3375 g/mL
ρ ≅ 0.338 g/mLOPTION A
(A) Find the average velocity (the average rate of change of y with respect to x ) for x changing from 3 to 9 seconds. Don't forget to include units in all your answers. Average velocity = (B) Find the average velocity for x changing from 5 to 5+h seconds. Average velocity = (C) Find the instantaneous velocity at x=5 seconds. Instantaneous velocity = Suppose that an object moves along the y-axis so that its location is y=x 2
+5x at time x. (Here y is in meters and x is in seconds.) (A) Find the average velocity (the average rate of change of y with respect to x ) for x changing from 3 to 9 seconds. Don't forget to include units in all your answers. Average velocity = (B) Find the average velocity for x changing from 5 to 5+h seconds. Average velocity = (C) Find the instantaneous velocity at x=5 seconds. Instantaneous velocity =
(A) The average velocity for x changing from 3 to 9 seconds is 13 meters per second. (B) The average velocity for x changing from 5 to 5+h seconds is 10h + 5 meters per second. (C) The instantaneous velocity at x=5 seconds is 25 meters per second.
(A) To find the average velocity, we need to calculate the change in y divided by the change in x. In this case, y = x^2 + 5x. Evaluating y at x = 3 and x = 9, we have y(3) = 36 and y(9) = 126. The change in y is 126 - 36 = 90. The change in x is 9 - 3 = 6. Therefore, the average velocity is 90/6 = 15 meters per second.
(B) The average velocity for x changing from 5 to 5+h seconds can be found by evaluating the function y = x^2 + 5x at x = 5 and x = 5+h, and then calculating the change in y divided by the change in x. Substituting these values, we have y(5) = 50 and y(5+h) = (5+h)^2 + 5(5+h). Simplifying, we get y(5+h) = h^2 + 15h + 50. The change in y is h^2 + 15h, and the change in x is h. Therefore, the average velocity is (h^2 + 15h)/h = h + 15 meters per second.
(C) To find the instantaneous velocity at x=5 seconds, we take the derivative of the function y = x^2 + 5x with respect to x. The derivative is dy/dx = 2x + 5. Evaluating this derivative at x = 5, we get dy/dx(5) = 2(5) + 5 = 15. Therefore, the instantaneous velocity at x=5 seconds is 15 meters per second.
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