On a day when the wind is blowing toward the south at 3 m/s, a runner jogs west at 4 m/s. What is the speed of the
air relative to the runner?
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]{\sf {V}_{w} } [/tex]= velocity of wind = 3 m/s (south) [tex]{\sf {V}_{r} } [/tex]= velocity of runner = 4 m/s (west)So,
[tex]{\sf {V}_{w} } [/tex] = - 3 [tex]{ \sf \hat{j}} [/tex][ taking unit vector along north be [tex]{ \sf \hat{j}} [/tex] ]
[tex]{\sf {V}_{r} } [/tex] = - 4 [tex]{ \sf \hat{i}} [/tex][ taking unit vector along west be [tex]{ \sf \hat{i}} [/tex] ]
[tex] \qquad \dashrightarrow\sf \: V_{wr}= V_{w} - V_{r }[/tex]
[ where [tex]{ \sf V_{wr}= } [/tex] Relative velocity of wind with respect to runner ]
[tex] \qquad \dashrightarrow\sf \: V_{wr}= - 3 \hat{ j} - ( - 4 \hat{i})[/tex]
[tex] \qquad \dashrightarrow\sf \: V_{wr}= - 3 \hat{ j} + 4 \hat{i}[/tex]
That is : 3 m/s towards south and 4 m/s towards east.
So, it makes an angle of 37° with south, and 53° with East.
[ The resultant is depicted by yellow arrow in attachment ]
Magnitude :[tex] \qquad \dashrightarrow\sf \: |V_{wr} | = \sqrt{3 {}^{2} + 4 {}^{2} }[/tex]
[tex] \qquad \dashrightarrow\sf \: |V_{wr} | = \sqrt{9 + 16 }[/tex]
[tex] \qquad \dashrightarrow\sf \: |V_{wr} | = \sqrt{25 }[/tex]
[tex] \qquad \dashrightarrow\sf \: |V_{wr} | = 5 \: \: m/s[/tex]
Direction :[tex] \dashrightarrow \sf \tan( \alpha) = \dfrac{b\: \sin \theta}{b + a \sin( \theta) } [/tex]
[tex]{\sf \theta }[/tex] = angle between the two vectors ( along east and south) i.e 90°
b = 4 units[tex] \dashrightarrow \sf \tan( \alpha) = \dfrac{4\: \sin (90 \degree)}{3+ 4 \cos( 90 \degree) } [/tex]
[tex] \dashrightarrow \sf \tan( \alpha) = \dfrac{4 \times 1}{3+( 4 \times 0)} [/tex]
[tex] \dashrightarrow \sf \tan( \alpha) = \dfrac{4}{3} [/tex]
[tex] \dashrightarrow \sf \alpha = \tan {}^{ - 1} \bigg( \dfrac{4}{3 } \bigg)[/tex]
[tex] \dashrightarrow \sf \alpha = 53 \degree[/tex]
So, it's direction is 53° east from south ~
76. Two electric charges -6μC and
+6μC are placed respectively in two
points A and B distant of 1m apart. The
electric field is null at the point C:
A.Located in the middle of the
segment AB
B.Located outside segment AB at
1m from A.
C.Located outside segment AB at
1m from B
D.Outside the line AB
E.No answer is right.
Answer:
D. Located outside line AB
Explanation:
I do not have a Columb table with me, so it could be B. or C., but if I did the math right, then I think the answer is D.
The surface of the pool table is ℎ=0.790 m from the floor.
The winner of the competition wants to know if he has broken the world speed record for the break shot of 32 mph (about 14.3 m/s ). If the winner's ball landed at a distance of =5.05 m from the table's edge, calculate the speed of his break shot 0. Assume friction is negligible.
At what speed 1 did his pool ball hit the ground?
The calculated velocity is 3.88 m/s
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value. The parameters of speed are time divided by distance. The most often used unit of speed in daily life is the kilometer per hour (km/h), or miles per hour in the US and the UK. The SI's unit of speed is the meter per second (m/s) (mph).
h = 0.5g*t² = 0.77 4.9t²
= 0.77\st²
= 0.1571
t = 0.396 seconds or fall.
Dx = Xo*t, or 5.15 meters.
Xo * 0.396 = 5.15
Break speed is X= 13 m/s.
V² = V² + 2g*h.
V² = 0 + 19.6*0.77
= 15.09
V = 3.88 m/s
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Is the suns gravitational pull on the earth the same at all seasosons of the year
No, the sun's gravitational pull is not same at all seasons of the year
The gravitational force between the Sun and Earth depends on the earth's distance from the sun and hence it varies over the course of a year. This is because the Earth’s orbit is an ellipse, bulged at the poles like an orange rather than a perfect circle. Earth’s average distance from the sun is approximately 150 million km , closest distance to the Sun is 146 million km, the largest distance is about is 152, so the distance varies by about 5.
The gravitational force between two bodies depends on their mass (how heavy they are) and their distance, and the distance changes according to the rotation an d revolution of the earth around the sun so the gravitational force also varies.
Earth revolves around the sun in its elliptical orbit and hence the force is balanced out due to certain factors and does not spiral out from its orbit. The change in gravitational force is balanced out due to certain factors such as change in speed of rotation and more and hence the gravitational pull on the earth is not the same .
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What is the largest structure people have put into space?
Hubble Space Telescope
International Space Station
Space Shuttle
Mars rover Curiosity
Answer:
International Space Station
Explanation:
I did the test and I’m 100% sure
Answer:
b) International Space Station
Explanation:
International Space Station (ISS) is the largest structure, which people have put into space. Hence, option (b) is correct.
True or False—The vector for a negative acceleration points in the opposite direction when compared to the vector for a positive acceleration.
Answer:
True
Explanation:
Opposites point in opposite directions
2. How long will it take for a bicycle to travel across from point A to
point D as shown below in the figure if his velocity was 4 m/s. Hint: use
Pythagorean Theorem () to find your displacement. A²+ B² = (²
A
25m
B
25m
D
35m
C
V = & Devt T=B
Answer:
I guess equal to ABD
Applying a constant net force to an object causes it to accelerate at 0=9.0 m/s2.
What will the acceleration 3 of the object be if the force is doubled and the mass is doubled?
The acceleration of the object be if the force is doubled and the mass is doubled is equal to 9m/s².
let the initial mass of the object be m₁.
given:
initial acceleration (a₁) = 9m/s²
initial constant force (F₁) = constant (k)
therefore,
F₁= m₁×a₁ ------------------------------- equation 1
now,
according to the the question the force is doubled
i.e.
new force (F) = 2×F₁
and the mass too is doubled,
i.e.
new mass of the object(m)=2×m₁
new equation for force and acceleration:
F= m ×a
2F=2m₁×a --------------------------equation 2
dividing equation 2 by equation 1
we get,
[tex]\frac{2F}{F}=\frac{2m₁×a}{m₁×a₁ }[/tex]
a = a₁
a=9m/s²
the acceleration of the object be if the force is doubled and the mass is doubled is equal to 9m/s².
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What was Einstein Seeking?
Einstein was seeking a way to unify electromagnetism and gravity into a single theory.
After all the breakthroughs given by Einstein, he then worked on a " Grand Unified theory" for the last thirty of his life. He believed that all the forces of nature ( Electromagnetism and gravity were the only forces discovered at that time ) must be described by a single theory.
He failed to figure out a way to unify the forces of nature under a single theory. But physicists, even to this day are still working on the Grand Unified theory.
Therefore, Einstein was seeking a way to unify electromagnetism and gravity into a single theory.
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Carry out these steps, and record your findings in the table.
1. Pour water to the 2.0 mL mark in the graduated cylinder. If you look at the graduated cylinder from
the side, you will see the water forms a curve, Make sure the bottom of the curve is at the 2.0 mL
mark.
2. Use the gram scale to measure the mass of the graduated cylinder and 2.0 mL of water. Record the
mass in the table. Calculate the mass of 2.0 mL of water by subtracting the mass of the graduated
cylinder.
3. Repeat this process to find and record the mass of 4.0 mL of water and then 6.0 mL of water.
4. Density is mass in grams divided by volume in cubic centimeters (cm³). 1 mL
d = M/V, where d is density, M is mass, and V is volume, is the formula for density. Grams per cubic centimeter are a typical unit of measurement for density.
To fill the graduated cylinder to the 2.0 mL mark, add water. The water makes a curve if you see the graduated cylinder from the side. Make sure the 2.0 mL level is at the bottom of the curve. Calculate the graduated cylinder's mass and the water's mass in milliliters using the gram scale. In the table, note the mass. Subtract the graduated cylinder's mass to determine the mass of 2.0 mL of water. To find and note the mass of 4.0 mL of water, repeat this procedure.
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A rectangular box is h = 8.5 inches in height, w = 36.5 cm wide, and L = 0.55 yards long.
Please help!!!
The volume of the rectangular box is 39559.36 cm³.
What is volume?Volume can be defined as the capacity of a solid substance. The S.I unit of volume is m³.
To calculate the volume of the rectangular box, we use the formula below.
Formula:
V = lwh................... Equation 1Where:
V = Volume of the rectangular boxl = Length of the boxw = Width of the boxh = Height of the boxFrom the question,
Given:
l = 0.55 yards = 50.2 cmw = 36.5 cmh = 8.5 inches = 21.59 cmSubstitute these values into equation 1
V = (50.2×36.5×21.59)V = 39559.36 cm³Hence, the volume of the rectangular box is 39559.36 cm³.
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True or false - The vector for a negative acceleration points in the opposite direction when
compared to the vector for a positive acceleration.
Explanation:
the ratio between two circles vqjoizxcvu g çm
What is the total capacity in gallons of a rectangular tank 5 meters in height knowing that it will hold 200 liters per foot?
The total capacity in gallons of the rectangular tank is 866.58 gallons
How to find the total capacity in gallons of the rectangular tank?Since the rectangular tank is 5 meters in height knowing that it will hold 200 liters per foot, we need to know the total capacity of water it contains for the height of 5 meters.
Converting 5 m to feet, we have
Since 1 m = 3.28 ft, we have
5 m = 5 × 1 m = 5 × 3.28 ft = 16.4 ft
Since the height of the tank in feet is 16.4 ft and the tank holds 200 L/ft, then the total capacity of water in 16.4 ft is D = 200 L/ft × 16.4 ft
= 3280 L
To know the total capacity of the tank in gallons,we convert 3280 L to gallons
Since 1 L = 0.2642 gallons, converting 3280 L to gallons, we have
3280 L = 3280 × 1 L = 3280 × 0.2642 gallons
= 866.576 gallons
≡ 866.58 gallons
So, the total capacity in gallons of the rectangular tank is 866.58 gallons
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What is the average velocity of the object?
______ m/s
Answer:
0.1 m/s (or 100 cm/s)
Explanation:
At the first point on the graph’s faded grid, the object has traveled 1 meter in 10 seconds. At the next point, the object traveled 2 meters in 20 seconds. This is a 1 to 10 ratio, or 1/10, which is 0.1 in decimal format.
Can you give me the reference frame for every one of these please.
The sun rises over the horizon.
A bus moves past people standing on the sidewalk.
A passenger on that same bus sees a ball roll down the aisle.
Two trains traveling at the same speed on parallel tracks race past passengers who are waiting on a local station's platform.
A passenger on one of those trains looks out the window and sees the other train standing still.
A person standing near a railroad track sees a train pass by, then notices an airplane fly overhead in the same direction as the train, but at a much faster speed.
A passenger in that airplane looks down and sees the train moving backward.
A passenger in that airplane looks across the aisle and sees a child tossing a ball up and down.
A bus moves past people standing on the sidewalk, reference frame is people on the sidewalk.A passenger on that same bus sees a ball roll down the aisle, reference frame is the train aisle.
Two trains traveling at the same speed on parallel tracks race past passengers who are waiting on a local station's platform, reference frame is the station's platform.
A passenger on one of those trains looks out the window and sees the other train standing still, reference frame is the other train standing still.
A person standing near a railroad track sees a train pass by, then notices an airplane fly overhead in the same direction as the train, but at a much faster speed, reference frame is railroad track.A passenger in that airplane looks down and sees the train moving backward, reference frame is inside of the airplane.A passenger in that airplane looks across the aisle and sees a child tossing a ball up and down, reference frame is the aisle.
What is reference frame?
Reference frame can be described as the stationary background to which an object is compared to tell if it is moving.
A frame of reference is therefore a purely kinematical device, for the geometrical description of motion without regard to the masses or forces causing the motion.
The instance we discussed had different reference frames all of which are the stationary background of the objects.
In conclusion, reference frame of an object describes the motion without regard to the forces causing the motion.
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A weight is suspended motionless from a bar which hangs from the ceiling by two ropes. The
weight has 25 N of gravitational force pulling on it. A free-body diagram for this situation looks
like this:
Answer: a weight of 25n
Explanation:4+5
An atom is most balanced when it has an equal number of protons and electrons. True False
Answer: It is true.
Explanation: In all atoms, the number of electrons and protons is always equal. This preserves the atom's electrical neutrality by balancing positive and negative charges. If the amount of electrons and protons in an atom is not equal, the atom will have a net positive or negative charge, forming a cation or an anion.
find the number of significant figures in the following product:
0.005032 x 4.0009
The number of significant figures in the following product: 0.005032 x 4.0009 is 9.
What is significant figure?Significant figure is a figure that is meaningful with respect to the precision of a measurement.
It is a digit that is nonzero, followed by a nonzero digit, or (for trailing zeroes) justified by the precision of the derivation or measurement.
According to this question, the product of 0.005032 x 4.0009 is as follows: 0.0201325288
The result of this product is as follows:
Decimal notation: 0.0201325288No. of significant figures: 9No. of decimals: 10Scientific notation: 2.01325288 × 10-²Therefore, the number of significant figures in the following product: 0.005032 x 4.0009 is 9.
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A book is at rest on a table top. The gravitational force acting on it is 100 N. A free-body
diagram for this situation looks like this:
Answer: 100n
Explanation: 1+1=2
2. The longest snake ever found was a python that was 10.0 m long. Sup-
pose a coordinate system large enough to measure the python's length is
drawn on the ground. The snake's tail is then placed at the origin and the
snake's body is stretched so that it makes an angle of 60.0° with the posi-
tive x-axis. Find the x and y coordinates of the snake's head. (Hint: The y-
coordinate is positive.)
Answer:
See below
Explanation:
Hypotenuse is snake length 10 m
y coordinate = 10 sin 60 = 8.7 m
x coordinate = 10 cos 60 = 5m
The more exercise a person takes the fewer medical problems they report. This is an example of:
O A. statistical independence.
B. a positive correlation.
O C. a negative correlation.
D. a curvilinear relationship
Answer:
The best answer seems to be B because there is a strong positive correlation that the more exercise a person does, the fewer medical problems they have
Explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
The more exercise a person takes the fewer medical problems they report. This is an example of a positive correlation. The correct option is B.
What is positive correlation?When two variables rise or decrease simultaneously, there is a positive correlation; when there is a negative correlation, one variable increases as the other falls.
When two variables behave in unison, rising or falling in lockstep with one another, there is a positive correlation.
When two variables move in opposition to one another—that is, when one rises, the other falls—this is known as a negative correlation.
A person reports fewer medical issues the more activity they get. An illustration of a positive correlation would be this.
Thus, the correct option is B.
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What is the temperature of an object where it is half as hot as 80°F?
Answer:
See below
Explanation:
In absolute temperature 80 F = 299.82 K
1/2 of this is 149.9 K = - 189.84 degrees F
- 189.84° F is the temperature of an object where it is half as hot as 80°F. A thermometer or even a calorimeter can be used to measure it.
What is temperature?The temperature of a thing is an absolute measure as to how warm or cold it is. A thermometer or even a calorimeter can be used to measure it. It is a method for determining actual internal energy of a particular system.
Temperature is an aspect of reality which we have a reasonably intuitive grasp on since humans easily detect the quantity of heat and cold inside an area. Although the two notions are related, temperature is distinct from heat. Temperature is a measurement of a system's intrinsic energy.
In absolute temperature
80 F = 299.82 K
1/2 of this is 149.9 K = - 189.84° F
Therefore, - 189.84° F is the temperature of an object where it is half as hot as 80°F.
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An 80% furnace's discharge air temperature is 125 degrees F and is adding heat to a space at the rate of 80,000 BTU's an hour. What is the input rating of the furnace?
a. 60,000 Btu's
b. 120,000 Btu's
c. 75,000 Btu's
d. 100,000 Btu’s
D. The input rating of the furnace is determined as 100,000 BTU.
What is input rating?Input power rating means the power, expressed in Watts or one of its multiples, for which the energy storage unit has been designed to operate at nominal conditions.
eff = (output rating / input rating) x 100%
80/100 = 80,000 BTU / input rating
0.8 = 80,000 BTU / input rating
input rating = 80,000 BTU/0.8
input rating = 100,000 BTU
Thus, the input rating of the furnace is determined as 100,000 BTU.
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Yodi had 5 apples, if yodi has 5 apples and gives away 4, how many apples does yodi have left?
This is based on probability since it is obvious that I have 4 apples if I take away 4 of them.
What does PROBABILITY mean?Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only forecast how likely an event is to occur using it, or how likely it is to occur..
provided the information; one apple. 5–4=1. Your teacher is looking for this response.
According to given information;
The four apples you took total four. Probably the one you want is this.
No apples; they were taken from you.
You gave your friend the entire crop of apples.
The fruits you discarded had worms, therefore you got zero apples.
a trio of apples. You missed one.
One apple. You ate two and cut up one of them for a salad.
Five apples. You had 5 apples and you took 4 of your own.
Five apples. You already had an apple.
Six apples. You already had two apples.
Seven apples. You already had three apples.
Eight apples. You already had four…
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which statement would need to be true for astrology to be considered a science?
A. Experimental evidence is collected that supports that astrology is to be considered a science.
Which statement best describes that the astrology is the part of science?Through experiments and researches, we can collect a lot of evidences about the relationship between science and astrology. If the evidences are in favour of astrology so we can say that astrology is to be considered as science. The invention of the astrology was made in Babylon far back in antiquity. An astrology is not considered to be the part of the science, because there is no evidence present in the history that the astrology is the part of the science. But the main thing is that the astrology contains the logics, and logics is present in the science. So there is a very small relation between the astrology and the science.
So we can conclude that Experimental evidence is collected that supports it is the correct statement.
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A. Experimental evidence is collected that supports it.
B. The majority of people believe that its claims are true.
C. Its explanations are supported by a scientific law.
d. Government funding is used to support it.
If a rocket initially at rest accelerates at a rate of 49.3 m/s/s for 8.7 seconds, its speed will be
decimal place.
Answer:
428.9 m/s
Explanation:
Vf = at = 49.3 m/s^2 * 8.7 s = 428.9 m/s
Liz rushes down onto a subway platform to find her train already departing. She stops and watches the cars go by. Each car is 8.60 m long. The first moves past her in 1.80 s and the second in 1.61 s. Find the constant acceleration of the train.
The constant acceleration of the train is 0.33 m/s.
The average velocity can be calculated by using the formula:
velocity = distance/time
For the 1st car, the velocity is calculated as:
v₁ = 8.60 m / 1.80 s = 4.78 m / s
For the second car, velocity can be calculated as:
v₂ = 8.60 m / 1.66 s = 5.34 m / s
Now we can solve for the acceleration using the formula:
v₂² = v₁² + 2 a d
Rewriting in terms of a, we get
a = (v₂² – v₁²) / 2 d
a = (5.34)² – (4.78)² / (2 × 8.6)
a = 0.33 m/s
Therefore, the constant acceleration of the train is 0.33m/s.
what is acceleration explain?
acceleration, fee at which speed modifications with time, in terms of each pace and course. A factor or an object shifting in a directly line is improved if it hastens or slows down. motion on a circle is improved even if the velocity is steady, due to the fact the route is constantly converting
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The driver of a car slams on the brakes, causing the car to slow down at a rate of 17.0ft/s2 as the car skids 172ft to a stop
How long does the car take to stop?
What was the car's initial speed?
The time taken for the car to stop is 4.5 seconds and the initial speed of the car is 76.47 ft/s.
Initial speed of the carThe initial speed of the car is calculated as follows;
v² = u² + 2as
where;
v is the final velocity, when the car stops, v = 0u is the initial velocitya is the accelerations is the distance traveled0 = u² + 2as
0 = u² + 2(-17)(172)
0 = u² - 5858
u² = 5848
u = 76.47 ft/s
Time of motion of the carv = u + at
0 = 76.47 - 17t
17t = 76.47
t = 4.5 seconds
Thus, the time taken for the car to stop is 4.5 seconds and the initial speed of the car is 76.47 ft/s.
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A body of mass 20g performs simple harmonic motion at a frequency of 10Hz. Its position is 10cm from the mean position, calculate its velocity
if a bird catches its prey from a height which was initially at rest then momentum is conserved for?
Bird
Prey
Both
None
For the two animals involved (bird and its prey), the momentum of both animals is conserved.
What is principle of conservation of linear momentum?
The principle of conservation of momentum states that if two objects collide, then the total momentum before and after the collision will be the same if there is no external force acting on the colliding objects.
Initial momentum = final momentum
Thus, for the two animals involved (bird and its prey), the momentum of both animals is conserved.
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