You are standing on a river bank. The river is flowing at a rate of $2.0\;\mathrm{ m/s}.$ You see a duck is floating in the river without swimming, and is being carried by the river downstream. You throw two pieces of bread at the duck. One piece lands upstream of the duck, and the other downstream equal distance. The duck can swim at $1.0 \; \mathrm{m/s}.$ The duck is hungry, and wants to reach the bread in the shortest amount of time. What should the duck do
Let the upstream breadcrumb's position act as the origin, so the position at time [tex]t[/tex] of upstream crumb [tex](B_U)[/tex], duck [tex](D)[/tex], and downstream crumb [tex](B_D)[/tex] are, respectively,
[tex]x_{B_U} = \left(2.0\dfrac{\rm m}{\rm s}\right) t[/tex]
[tex]x_D = d\,\mathrm m + v_D t[/tex]
[tex]x_{B_D} = 2d\,\mathrm m + \left(2.0\dfrac{\rm m}{\rm s}\right) t[/tex]
where [tex]d[/tex] is the distance (in m) between the duck and either crumb at the start, and [tex]v_D[/tex] is the velocity of the duck relative to the Earth.
To get both breadcrumbs, the duck has to choose between chasing the upstream or downstream crumb first.
• If the upstream crumb is chosen first, then [tex]v_D[/tex] is 2.0 - 1.0 = 1.0 m/s. Find the time it takes for the duck to reach the upstream crumb:
[tex]x_{B_U} = x_D \implies \left(2.0\dfrac{\rm m}{\rm s}\right) t = d + \left(1.0\dfrac{\rm m}{\rm s}\right) t \\\\ \implies t = d \, \mathrm s[/tex]
In this time, the duck covers a distance of
[tex]x_D = d\,\mathrm m + \left(1.0\dfrac{\rm m}{\rm s}\right) (d\, \mathrm s) = 2d \, \mathrm m[/tex]
while the downstream crumb will have traveled a distance of
[tex]x_{B_D} = 2d\,\mathrm m + \left(2.0\dfrac{\rm m}{\rm s}\right) (d \,\mathrm s) = 4d \,\mathrm m[/tex]
putting a total distance of [tex]2d+4d=6d\,\mathrm m[/tex] between the duck and the remaining crumb.
Take the duck's new position to be the new origin. When the duck turns around and travels with the current, its speed [tex]v_D[/tex] will be 2.0 + 1.0 = 3.0 m/s. Then at time [tex]t[/tex], the duck and remaining crumb have position relative to the new origin given by
[tex]x_D' = \left(3.0\dfrac{\rm m}{\rm s}\right) t[/tex]
[tex]x_{B_D}' = 6d \,\mathrm m + \left(2.0\dfrac{\rm m}{\rm s}\right) t[/tex]
Find the time the duck needs to catch up to the downstream crumb:
[tex]x_D' = x_{B_D}' \implies \left(3.0\dfrac{\rm m}{\rm s}\right) t = 6d\,\mathrm m + \left(2.0\dfrac{\rm m}{\rm s}\right) t \\\\ \implies t = 6d \,\mathrm s[/tex]
Then the total time the duck needs to get both crumbs is [tex]d + 6d = 7d \,\mathrm s[/tex].
• If instead the downstream crumb is chased down first, we start with [tex]v_D[/tex] = 3.0 m/s, so that
[tex]x_D = x_{B_D} \implies d\,\mathrm m + \left(3.0\dfrac{\rm m}{\rm s}\right) t = 2d\,\mathrm m + \left(2.0\dfrac{\rm m}{\rm s}\right) t \\\\ \implies t = d \, \mathrm s[/tex]
In this time, the duck covers a distance of
[tex]x_D = d\,\mathrm m + \left(3.0\dfrac{\rm m}{\rm s}\right) (d\,\mathrm s) = 4d \,\mathrm m[/tex]
while the upstream crumb moves
[tex]x_{B_U} = \left(2.0\dfrac{\rm m}{\rm s}\right) (d\,\mathrm s) = 2d \,\mathrm m[/tex]
The distance between the duck and remaining crumb is then [tex]4d-2d=2d\,\mathrm m[/tex]. Now the duck turns around with speed [tex]v_D[/tex] = 1.0 m/s. If the crumb's new position is taken to be the origin, then
[tex]x_{B_U}' = \left(2.0\dfrac{\rm m}{\rm s}\right) t[/tex]
[tex]x_D' = 2d\,\mathrm m + \left(1.0\dfrac{\rm m}{\rm s}\right) t[/tex]
Find the time it takes for the duck to get the last crumb:
[tex]x_{B_U}' = x_D' \implies \left(2.0\dfrac{\rm m}{\rm s}\right)t = 2d\,\mathrm m + \left(1.0\dfrac{\rm m}{\rm s}\right) t \\\\ \implies t = 2d\,\mathrm s[/tex]
Then the duck can get both crumbs in a total of [tex]d+2d=3d\,\mathrm s[/tex].
To get both crumbs in the shortest time, the duck should go after the downstream crumb first. This path over 2 times faster than the other.
State a hypothesis about what might happen as you proceed through the lab.
A hypothesis about what might happen in the lab might be 'oxygen will react with hydrogen to form water molecules'.
What is a hypothesis?A hypothesis is a given explanation of a particular scientific question emerged by observing the real world.
Hypotheses are explanations that must be tested (either confirmed or rejected) by using the scientific method.
In conclusion, a hypothesis about what might happen in the lab might be 'oxygen will react with hydrogen to form water molecules'.
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A 740 kg car traveling 19 m/s comes to a complete stop in 2.0 s. What is the force exerted on the car during this stop?
Answer:
Force exerted on the car is 7030 N.
Explanation:
It is given that,
Mass of the car, m = 740 kg
Initial speed of the car, u = 19 m/s
Final speed of the car, v = 0
Time taken, t = 2 s
Let F is the force exerted on the car during this stop. We know that it is equal to the product of force and acceleration. Mathematically, it is given as :
F=m\times \dfrac{v-u}{t}F=m×tv−u
F=740\times \dfrac{0-19}{2}F=740×20−19
F = -7030 N
So, the force exerted on the car during this stop is 7030 N. Hence, this is the required solution.
The chart shows the times and accelerations for three drivers.
A 3-column table with 3 rows. The first column labeled drover has entries Kira, Dustin, Diego. The second column labeled acceleration has entries 5.2 meters per second, 8.3 meters per second, 6.5 meters per second. The third column labeled time has entries 6.9 seconds, 3 seconds, 4.2 seconds.
Which lists them from greatest to lowest change in velocity?
Dustin → Diego → Kira
Dustin → Kira → Diego
Kira → Dustin → Diego
Kira → Diego → Dustin
The lists from greatest to lowest change in velocity.Dustin → Diego → Kira. Option A is correct.
What is acceleration?The rate of change of velocity with respect to time is known as acceleration. According to Newton's second law, the eventual effect of all forces applied to a body is its acceleration.
The acceleration is obtained one by one from the given data as the ratio of the velocity to the time.
For the acceleration of each, you can refer to the excel table attached below.
The velocity changes are listed from largest to least. Dustin and Diego Kira.
Hence, option A is the right answer.
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Answer:
D. Kira → Diego → Dustin
Explanation:
Got 100% on the test. Y'all have a good day! :p
Two particles with oppositely signed charges nC are placed at two of the vertices of an equilateral triangle with side length 3 m. What is the magnitude of the electric field at the third vertex of the triangle
The magnitude of the electric field at the third vertex of the triangle is determined as zero.
Electric field at the third vertex of the triangle
The electric field at the third vertex of the equilateral triangle due to the other charges placed on the first and second vertices is calculated as follows;
E = E(13) + E(23)
E = (kq₁)/r² + (kq₂)/r²
where;
q1 is positive chargeq2 is negative chargeE = (kq₁)/r² - (kq₂)/r²
E = 0
Thus, the magnitude of the electric field at the third vertex of the triangle is determined as zero.
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Which two elements have the same number of dots around their chemical symbols in their electron dot disgrams?
The two elements that have the same number of dots around their chemical symbols in their electron dot are Germanium and Silicon.
Dot diagram of elements
The valence electron of an atom can be represented by a lewis dot diagram.
Germanium and silicon belonging to group 14 of the periodic table has 4 dots around their chemical symbols in their electron dot.
Thus, the two elements that have the same number of dots around their chemical symbols in their electron dot are Germanium and Silicon.
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The diameter of the Earth is 12.7 x 10 6 m. The diameter of Mars is 6800 km.
The difference in the diameters of the two planets is:
Answer:
5.9 × 10⁶m
Explanation:
The diameter of the Earth is 12.7 ×10⁶m.We have to convert the diameter of the mars in the same exponent as that of the earth so that we can easily subtract.The diameter of mars = 6800km = 6800 × 10³ m = 6.8 × 10⁶mNow we can subtract the diameters.The difference between the diameters = (The Diameter of Earth - The diameter of Mars)= 12.7×10⁶ - 6.8 × 10⁶
= 5.9 × 10⁶m
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What name carries the hypothetical artificial megastructure surrounding a star in order to capture its power?.
Question 2 of 34
You are adding two vectors pointing in the same direction. How do you find
the magnitude of the resultant vector?
OA. By subtracting the magnitude of the shorter vector from the
magnitude of the longer vector
B. By adding the magnitudes of the two vectors
O C. By subtracting the magnitudes of the two vectors
D. By subtracting the magnitude of the longer vector from the
magnitude of the shorter vector
You can find the magnitude of the resultant vector : (B). By adding the magnitudes of the two vectors
Meaning of Vectors
A vector can be defined as any quantity which possesses magnitude and also has direction.
A Vector quantity is very useful because This type of quantity gives more details to the student or teacher analyzing it.
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1. What is the relationship between mass, weight and gravity?
Answer:
Mass
The kilogram (kg) is the SI unit of mass and it is the almost universally used standard mass unit.
Gravity and weight
Since the acceleration due to the force of gravity (g) equals aproximately 9.8 meters/s2, the weight of an object with a mass of 1 kilogram is 9.8 newtons under standard conditions on the Earth's surface.
Answer:
The mass of an object is a measure of the object's inertial property, or the amount of matter it has in it
The weight of an object is a measure of the force/impact exerted on the object by gravity, or the force needed to support it
The pull of gravity on the earth gives an object a downward acceleration of about 9.8 m/s2.
Hope This Helped
If it takes you 10 seconds to move a chair 5 meters across the floor, using a force of 2 Newtons, how much power did you put out?
20 joules per second
100 joules per second
O 1 joules per second
4 joules per second
Answer:
power=work done÷time taken
2×5=10
10÷10=1
ans 1J per second
a straight current-carrying wire in a uniform magnetic field, oriented at right angles to the wire. The 0.25-m wire carries a 4.75-A current and experiences a force of 0.38 N. What is the strength of the magnetic field?
0.45 T
0.56 T
0.32 T
0.72 T
Hello!
Using the equation for the magnetic force on a current-carrying wire:
[tex]F_B = \vec{B} \times i\vec{L}[/tex]
[tex]F_B[/tex] = Magnetic Force (0.38 N)
B = Magnetic field strength (T)
i = Current in wire (4.75 A)
L = Length of wire (0.25 m)
This is a cross product, so we can rewrite the equation as:
[tex]F_B = BiLsin\phi[/tex]
Where φ is the angle between the magnetic field vector and the length vector. In this instance, since the field is perpendicular to the wire, sin(90) = 1. We can simplify the equation to:
[tex]F_B = BiL[/tex]
Rearrange the equation to solve for 'B':
[tex]B = \frac{F_B}{iL}[/tex]
Plug in given values and solve.
[tex]B = \frac{0.38}{(4.75 * .25)} = \boxed{0.32 T}[/tex]
The strength of the magnetic field will be 0.32 T.Option B is correct.
What is magnetic field strength?The number of magnetic flux lines on a unit area passing perpendicular to the given line direction is known as induced magnetic field strength .it is denoted by B.
Given data:
(I) current = 4.75-A
(B)induced magnetic field strrength=?
(L)length of the wire=0.25-m
(F)Magnetic force=0.38 N
The strength of the magnetic field is found as:
[tex]\rm F_B=BILsin \theta \\\\\ \theta = 90^0 \\\\ \rm F_B=BIL \\\\[/tex]
Substitute the values:
[tex]\rm 0.38 = B \times 4.75 \times 0.25 \\\\\ B= \frac{0.38}{4.75 \times 0.25 } \\\\\ B=0.32 \ T[/tex]
The strength of the magnetic field will be 0.32 T.
Hence, option B is correct.
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A diffraction grating used in a spectrometer causes the third-order maximum of blue light with a wavelength of 490 nm to form at an angle of 6.33º from the central maximum (m = 0). What is the separation between the lines of the grating?
The separation between the lines of the grating is 13.33μm.
What is diffraction grating?The diffraction grating is the continuous lines with very minute slits or grating space in mm. It divides light composed of various wavelengths into light components by particular wavelength.
dsinθ = nλ
Substitute n =3, λ =490 x 10⁻⁹ m and angle θ =6.33°, we get
d = [3 x 490 x 10⁻⁹ /sin 6.33°]
d = 13.33 x 10⁻⁶ m
Thus, the separation between the lines of the grating is 13.33μm.
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why is physics the hardest subject
Explain how birds, bats, insects, airplanes, rockets, and hot air balloons achieve their flight.
The birds, bats, insects, airplanes, rockets, and hot air balloons achieve their flight by creating high pressure below the aircraft and low pressure above it
What are living and non-living things?They both consist of fundamentally simple building blocks. They are composed of substances or mass. Atmospheric and molecular building blocks make up the world.
In order to create high pressure below the aircraft and low pressure above it, airplanes employ specially built wings.
The wing receives sufficient airflow past it to counteract the weight and drag of the aircraft by utilizing a device to provide thrust, such as a propeller.
High pressure underneath the aircraft and low pressure above it is produced by specially constructed wings used by airplanes.
The wing receives enough airflow through it by the use of a thrust-generating device, like a propeller, to overcome the weight and drag of the aircraft.
The differences between how living and non-living things fly;
1. Moving both living and non-living objects consumes energy. Flying animals utilize their wings to create both lift and propulsion by moving them in relation to the body.
In contrast to most air vehicles, where the components that generate lift, wings, and thrust engines or propellers are distinct, the wings stay stationary.
Animal aviators like birds as well as natural parachuters like patagial as well as human inventions like aircraft as well as rockets that can power spacecraft and spaceplanes are just a few examples of the many things that can fly.
Hence, birds, bats, insects, airplanes, rockets, and hot air balloons achieve their flight by creating high pressure below the aircraft and low pressure above it
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How do riders in a Ferris wheel possess Translatory motion but not circular motion?
Answer:
A wheel on a car, however, rotates around the car's axle, so it does have rotational motion. For this example, if you were to pick a single point on the edge of the wheel, you could also say that it has circular motion.
The quarks that compose a baryon may have charges of:.
The quarks that compose a baryon may have charges of +(2/3)e and -(1/3)e which means have negative and positive charges.
What are quarks?Quarks are the most fundamental particles that make up the atomic nucleus. All solid matter that we know is made of three particles, which are the up and down quarks, 'u' and 'd', and the electron.
Quark is one of the two basic elements that make up matter and is the only one of the particles that interacts through all four fundamental forces.
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Try to solve this question:
Explanation:
w = mg
on earth
w = mg
w = 60 × 9.8 = 588 N
on moon
w = mg
w = 60 × 1.6 = 96 N
on Mars
w = mg
w = 60 × 3.7 = 222 N
In this question,we solve it using the formulae below:
W=mg.
So to find the weight of the object in 1.Earth.Enter the given data on formula:
W=mg
W=60×9.8
W= 588N.2.Weight on the moon.
W=mg
W=60×1.6
W=96N3.Weight on Mars.
W=mg
W=60×3.7
W=222N.Consider the soccer ball is kicked toward a goal at a speed of 35 mph and an angle of 25 ° from horizontal, what is the maximum height the ball will reach? Is this height more than a standard soccer goal's height, which is 8 feet from the ground?
(Recall: 1 mile = 1,609 meters and 1 hr = 3,600 s and 1 ft = 0.3048 meters)
The maximum height the ball will reach 7.316 ft. This height is less than a standard soccer goal's height.
What is projectile?When an object is thrown at an angle from the horizontal direction, the object is said to be in projectile motion. The object which follows the projectile motion is called the projectile.
Maximum height reached is given by
H = u²sin²θ /2g
where, u = initial velocity, θ is the angle of projection and g is the gravitational acceleration.
Consider the soccer ball is kicked toward a goal at a speed of 35 mph and an angle of 25 ° from horizontal,
Given is the speed 35mph = 35 x 1609/3600 = 15.65 m/s, θ =25 ° and g = 9.81 m/s²
Substituting the values, we get
H = (15.65)² (sin25 °)² / 2 x 9.81
H = 2.23 m
in feet, H = 7.316 ft
Thus, the maximum height is 7.316 ft. This height is less than a standard soccer goal's height, which is 8 feet from the ground.
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PLEASEE helppp I really need it!
Answer:
the correct answer is Jupiter has moons orbiting it
Olivia is on a swing at the playground.
A girl is swinging on a swing set. At W she is about 45 degrees up and to the left. At X she is near the bottom of the swing just to the left. At Y she is near the bottom of the swing just to the right. At Z she is about 45 degrees up and to the right.
If the swing is moving from W to Z, at which point is her kinetic energy increasing and her potential energy decreasing? (based on a starting point of W)
W
X
Y
Z
Mark this and return Save and Exit Next Submit
Olivia is on a swing at the playground. The kinetic energy is increasing and her potential energy decreasing at point X.
What is kinetic energy and potential energy?The kinetic energy of an object is the ability to do work by virtue of its motion and potential energy is the ability to do work by virtue of its position.
At point W and Z, Olivia is at the maximum displacement from the mean position, where kinetic energy is zero and potential energy is maximum.
At point Y, it is approaching to increase its potential energy and decreasing kinetic energy. Opposite to this, at point X, kinetic energy is increasing and potential energy is decreasing.
Thus, the kinetic energy is increasing and her potential energy decreasing at point X.
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Relate a real life phenomena with each branch of physics..
Answer:
Absolutely no real-life phenomena/ uses are possible that are related to any branch of physics, except:
1 The device you are reading this answer on. (quantum mechanics, electronics )
2 The air conditioner in your room. ( electromagnetism, electronics )
3 The satellites and space stations in space which will help in the deciphering of the universe will help us look for a suitable planet when we render the earth useless. ( general and special relativity, classical mechanics )
4 Ohh. I forgot, do you wear clothes, well they are made in factories where factories run on the principles of thermodynamics, which is physics.
5 Ever gone somewhere? Well, the transportation uses classical mechanics, thermodynamics, electromagnetism, relativity ( if you know Global Positioning System )
6 GPS itself! It’s used in online maps, navigating, and this sort of stuff. It works on general relativity.
Honestly, this list is endless.
For this situation, i push on a heavy chair. suppose i push moderately on the chair, and this time the chair does move. then the strength of the force the chair exerts on me is group of answer choices
What is a car’s acceleration if it increases its speed from 5 m/s to 20 m/s in 3 s? 10 m/s2 –15 m/s2 15 m/s2 5 m/s2
Answer:
5 m/s²
Explanation:
Acceleration = change in speed/time taken
20-5=15
15/3= 5 m/s²
a box is at rest on a ground. An unbalance force acts on the box causes it to start. The box moves 10 meters in 2 seconds and then stop. why did the box moving? what is the box's average speed?
A train traveling at 50m/s comes to a complete stop in 45 seconds. what was the rate of acceleration of the train?
The magnitude of the acceleration of the car is determined as 1.11 m/s².
Acceleration of the train
The acceleration of the train is determined as the rate of change of velocity with time.
The magnitude of the acceleration of the car is calculated as follows;
a = v/t
a = 50/45
a = 1.11 m/s²
Thus, the magnitude of the acceleration of the car is determined as 1.11 m/s².
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Use the information from the graph to answer the question.
A graph titled Velocity versus Time shows time in seconds on the x axis, numbered 0 to 12, velocity in meters per second on the y axis, numbered 0 to 45. A line starts at (0, 40) and ends at (12, 10).
What is the acceleration of the object?
Answer:-2.5m/s^2
Explanation:
facts
The acceleration of the object would be -2.5 m/s², the negative sign represents the deaccelerating motion of the object.
What is acceleration?The rate of change of the velocity with respect to time is known as the acceleration of the object. Generally, the unit of acceleration is considered as meter/seconds².
acceleration =change in velocity/change in time
The slope of the velocity time graph represents the acceleration of the object.
The slope of the graph = change in the y coordinates (velocity)/ change in the x coordinate (time)
The slope of the graph =( 10-40)/( 12-0)
= -2.5 m/s²
Thus, the acceleration of the object comes out to be -2.5 m/s².
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If you wanted to
reduce the resistance
in a circuit, what
should you do?
A. increase the length of the wire
B. replace a steel wire with a copper wire
C. replace a wide wire with a thin wire
Answer:
Option C
Explanation:
According to the formula
[tex]\\ \boxed{\sf R=\rho\dfrac{\ell}{A}}[/tex]So
If we use wide wire we increase the area of cross section so resistance decreases
A student on a tower 49 m height drops a stone. One second later he throws a second stone after the first. They both hit the ground at the same time, with what speed did he throw the second stone. [Ans: 10.1m/s]
By applying the second equation of motion, the speed at which he threw the second stone is equal to 12.10 m/s.
How to determine the speed?First of all, we would calculate the time taken by the first stone to reach a height of 49 meters by applying the second equation of motion as follows:
S = ut + ½gt²
49 = 0(t) + ½ × 9.8 × t²
49 = 4.9t²
t² = 49/4.9
t = √10
t = 3.16 seconds.
Now, we can determine the speed at which he threw the second stone:
Note: Time = 3.16 - 1 = 2.16 seconds.
S = ut + ½gt²
49 = u(2.16) + ½ × 9.8 × 2.16²
49 = 2.16u + 22.86
2.16u = 49 - 22.86
u = 26.14/2.16
u = 12.10 m/s.
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1. A person of mass 55 kg is in a bumper car that has a mass of 75 kg. They are together at a velocity of 8 m/s.
a. what's the total momentum of the system
b. what is the momentum of the bumper car after the collision? did it change directions? how do you know?
The momentum of the bumper car after the collision is 1,040 kgm/s.
Momentum of bumper
The change in momentum of the bumper is calculated as follows;
P = v(m1 + m2)
P = 8(55 + 75)
P = 1,040 kgm/s
The momentum of the bumper car after the collision is 1,040 kgm/s.
The direction is still the same.
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