To calculate the velocity of the plane relative to the ground, add up the x and y components of the plane's velocity and the wind velocity. Find the magnitude and direction of the resultant velocity using the Pythagorean theorem and trigonometry.
Explanation:To calculate the velocity of the plane relative to the ground, we need to consider the vector sum of the plane's velocity and the wind velocity. We can break down the velocity vectors into their x and y components. The plane's velocity is due south, so its x component is 0 km/h and its y component is -600 km/h. The wind velocity is blowing from the southwest, which can be represented as 45 degrees south of west. Its x component is -100*cos(45) km/h and its y component is -100*sin(45) km/h. Now we can add up the x and y components to find the resultant velocity vector. The x component is 0 + (-100*cos(45)) km/h and the y component is -600 + (-100*sin(45)) km/h. Finally, we can find the magnitude and direction of the resultant velocity vector using the Pythagorean theorem and trigonometry. The magnitude is sqrt(x^2 + y^2) km/h and the direction can be found using the arctan(y/x) function.
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A roller coaster starts from rest at point a and continues to point b on a frictionless track. what best describes the changes in kinetic and potential energy as the car travels from point a to point b?
Took a wild guess and got it correct. The answer is B Kinetic Energy increases and potential energy decreases.
The changes in kinetic and potential energy in a roller coaster from point A to point B on a frictionless track represent a conversion of potential energy into kinetic energy, with the total mechanical energy remaining constant.
As a roller coaster begins its journey from point A (at rest and at maximum height) to point B, it experiences a transformation of energy. Initially, at point A, the coaster has a maximum amount of gravitational potential energy (PE) because it is at its highest point. As the coaster moves to point B on the frictionless track, this potential energy is converted into kinetic energy (KE).
The law of conservation of energy states that the total mechanical energy in the system remains constant if we ignore losses due to friction. In this frictionless scenario, as the potential energy decreases while the coaster descends, the kinetic energy increases proportionally. By the time the coaster reaches point B, which is at a lower height, much of its original potential energy has been transformed into kinetic energy, giving it its highest speed.
Thus, the changes in kinetic and potential energy as the roller coaster travels from point A to point B can be described as a transfer where potential energy is converted into kinetic energy, and the total mechanical energy of the coaster remains constant.
A newly discovered gas has a density of 2.39 g/l at 23.0°c and 0.941 atm. what is the molar mass of the gas
The molar mass of the newly discovered gas is approximately 58.8 g/mol. This was calculated using the Ideal Gas Law and the gas's given density, temperature, and pressure.
Explanation:To determine the molar mass of a gas, you can use the Ideal Gas Law rearranged to solve for molar mass (M): = RT / , where 'm' is mass, 'R' is the gas constant, 'T' is temperature in Kelvin, 'P' is pressure, and 'V' is volume.
However, you can also use the given gas density (ρ = mass/volume = 2.39 g/L) and the Ideal Gas Law in a combined form: = / . So, the molar mass would be = (2.39 g/L * 0.0821 L atm/ K mol * (273.15 + 23.0)K ) / 0.941 atm = 58.8 g/mol.
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-Which of the following wires will have the least resistance?
A. A long thin wire
B. A short thin wire
C. A short thick wire
D. A long thick wire
...?
Answer:
Option (C)
Explanation:
The obstruction offered by the conductor in the path of flow of electrons is called the resistance of the conductor.
The reistance of the conductor is directly proportional to the length of the conductor and inversely proportional to the area of crossection of the conductor.
To minimize the resistance we need a wire of short length and more crossection area.
So, wire should be short and thick.
Heat is the transfer of thermal energy from one object to another because of a difference in
Which of the following best describes what causes the phases of the moon?
A. The alignment of the sun, Earth and moon (I think it's this one)
B. The speed of the moon around the Earth C. The speed of the Earth around the sun D. The alignment of the planets
A car travels 20 km west, then 20 km south. what is the magnitude of its displacement?
A) 0 km
B) 20 km
C) 28 km
D) 40 km
Answer:
The magnitude of its displacement of the car is 28 km.
Explanation:
It is given that,
Distance covered by the car due west, [tex]d_1=20\ km[/tex]
Distance covered by the car due south, [tex]d_2=20\ km[/tex]
We need to find the magnitude of its displacement. Let it is given by d. We know that displacement of an object is equivalent to the shortest path traveled. It can be calculated as :
[tex]d=\sqrt{d_1^2+d_2^2}[/tex]
[tex]d=\sqrt{(20)^2+(20)^2}[/tex]
d = 28.28 km
or
d = 28 km
So, the magnitude of its displacement is 20 km. Hence, the correct option is (c).
If gas in a cylinder is maintained at a constant temperature T, the pressure P is related to the volume V by a formula of the form P = ((nRT)/(V-nb))-((an^2)/(V^2)), in which a, b, n, and R are constants. Find dP/dV. ...?
The stopping distance d of a car after the brakes are applied varies directly as the square of the speed r. If a car travelling 70 mph can stop in 270 ft, how many feet will it take the same car to stop whenit is travelling 60 mph?
Situation:
A 30 gram sample of a substance thats used for to sterilize surgircal instruments has a k-value of 0.1253.
N=Noe^-kt
No=initial mass( at time t=0)
N=mass at time t
k=a positive constant that depends on the substance itself and on the units used to measure time
t=time, in days
Find the substance's half-life,in days.Round your answer to the nearest tenth. ...?
How many neutrons does element X have if its atomic number is 48 and its mass number is 167?
A stone is thrown downward with a velocity of 30.0 m/s from a cliff. if the height of the cliff is 100m, what velocity does it hit the ground?
The ability of an atom to attract the shared electrons in a covalent bond is its
A) bonding ability.
B) electronegativity.
C) polarity.
D) ionic character.
E) nonpolarity. ...?
Answer: electronegativity
Explanation: a covalent bond is a chemical bond. Electronegativity: an atom’s ability to attract shared electrons in a chemical bond (covalent bond is a chem bond).
A severe storm on January 10, 1992, caused a cargo ship near the Aleutian Islands to spill 29,000 rubber ducks and other bath toys into the ocean. Eight months later, hundreds of rubber ducks began to appear along a shoreline roughly 1800 miles away. What was the approximate average speed (in mi/h and m/s) of the ocean current that carried the ducks to shore? ...?
The average speed of the ocean current that carried the rubber ducks was approximately 0.309 miles per hour (mi/h) or 0.138 meters per second (m/s), calculated by dividing the total distance by the time taken and converting the units accordingly.
Explanation:The question revolves around calculating the average speed of ocean currents based on the distance rubber ducks traveled after being spilled into the ocean. To find the average speed, we divide the total distance by the total time taken. In this case, the ducks traveled approximately 1800 miles over eight months. Since one month averages about 30.44 days, and there are 24 hours in a day, we first convert 8 months into hours:
8 months * 30.44 days/month * 24 hours/day = 5825.92 hours
Now we calculate the average speed in miles per hour (mi/h):
Average Speed = Total Distance / Total Time = 1800 miles / 5825.92 hours = 0.309 mi/h
Next, we'll convert this speed into meters per second (m/s), using the conversion factor where 1 mile = 1609.34 meters.
0.309 mi/h * (1609.34 meters/mile) / (3600 seconds/hour) = 0.138 m/s
Therefore, the approximate average speed of the ocean current was 0.309 mi/h or 0.138 m/s.
What is the advantage of using a lever in lifting heavy objects over lifting them directly?
A. reduces the weight of the object
B. reduces the input force as well as alters the force in conveinent direction
C. alters the input force in a convenient direction
D. reduces the input force
The advantage of using a lever is that it reduces the input force required to lift a heavy object and can alter the direction of the force to be more convenient for the user. Option B is correct.
The advantage of using a lever in lifting heavy objects over lifting them directly is that it reduces the input force required to lift the object. A lever does this by changing the point where the force is applied and by increasing the distance over which this force is applied, making the work of lifting an object easier than lifting it directly. This principle of mechanics falls under the category of simple machines, which are devices that change the direction or magnitude of a force.
In the context of the multiple-choice question provided, the correct answer is : reduces the input force as well as alters the force in a convenient direction. This option accurately reflects the action of a lever—reducing the effort needed to lift a weight (input force) and changing the direction in which the force is applied to be more convenient for the user.
Where is information first stored in the human brain?
Final answer:
Information in the human brain is first stored in the hippocampus, which is crucial for converting short-term memory into long-term memory and for spatial navigation. The hippocampus works with other brain parts, like the cortex, for the long-term storage of information. Understanding hippocampus function helps underscore the importance of mental engagement and continuous learning.
Explanation:
Information in the human brain is first stored in the hippocampus, an essential part of the brain's limbic system. The hippocampus plays a critical role in the consolidation of information from short-term memory to long-term memory and spatial navigation. When we encounter new information, it is temporarily held in the sensory and short-term memory; if deemed important, this information is then transferred to the hippocampus for more durable storage. Over time, the process of memory consolidation involves the transfer of memories from the hippocampus to other parts of the brain for long-term storage, particularly to the cortex.
The formation and retrieval of memories involve a complex process that is not fully understood but is known to depend on various factors, including attention, emotional significance, and repetition. Neuroplasticity, or the brain's ability to reorganize itself by forming new neural connections, plays a vital role in learning and memory. This fascinating aspect of brain functionality underscores the importance of continuous learning and mental engagement for cognitive health.
In order to determine the power, you must know..
a. current and voltage
b. force and acceleration
c. newtons and joules
d. resistance and amperage
Answer:
option (a)
Explanation:
The electrical power is defined as the energy per unit time.
The formula foe the power is given by
P = V I = I^2 R = V^2 / R
So, to find the power we must know the values of current and voltage.
Answer:
The answer is <<< A. current and voltage
Explanation:
When the source of a sound is moving it's speed increases
Answer:
false
Explanation:
Higher energy efficiency is desirable because
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All of the following are areas of science EXCEPT
biology, the study of life
chemistry, the study of matter
astrology, the study of horoscopes
astronomy, the study of the universe
Which would show an example of how physical changes are reversible?
Which of the following elements is the least metallic in character
Which of the following is true about air pressure acting on an object?
a. The amount pushing down on the object will gradually decrease with time
b. The amount pushing up on the object will gradually increase with time
c. There is more air pressure pushing up on the object than there is pushing down
d. There is just as much air pressure pushing up as there is pushing down on the object
Answer: c. There is more air pressure pushing up on the object than there is pushing down
Explanation:
air pressure increases with air column above it. Thus, with increasing depth, the air pressure increases. Air pressure acts in all the directions. The bottom surface experiences greater air pressure than the top surface. Thus, there is more air pressure pushing up on the object than there is pushing down. correct option is c.
4786 joules fer transferred to an 89.0 gram sample of a unknown material with an initial temperature of 23.0°C what is the specific heat of the measure in the final temperature is 89.5°C
Answer:
0.8087 C J/g oC
Explanation:
4786 J = 89.0 g x C x (89.5 C- 23.0 C)
4786 J = 6185.5 gC
0.8087 C J/g oC
0.809 C J/g C (sig figs)
Final answer:
The specific heat of the unknown material, given the provided values, is calculated to be approximately 0.80 J/g°C.
Explanation:
To calculate the specific heat of the unknown material, we use the formula q = mcΔT, where q is the heat absorbed or released (in joules), m is the mass of the substance (in grams), c is the specific heat capacity (in Joules per gram per degree Celsius), and ΔT is the change in temperature (in degrees Celsius).
In this question, q = 4786 joules, m = 89.0 grams, and ΔT (change in temperature) = 89.5°C - 23.0°C = 66.5°C. Plugging in these values, we get 4786 = 89.0 * c * 66.5. Solving for c, we find that c = 4786 / (89.0 * 66.5).
After calculating, the specific heat of the material is found to be approximately 0.80 J/g°C.
What is the mechanical advantage of the machine?
All simple machines are variations of which two basic machines?
Final answer:
All simple machines are variations of the inclined plane or the lever, with examples like the wedge and the wheel and axle. They provide a mechanical advantage by multiplying the force applied. Complex machines, like bicycles, integrate multiple simple machines to increase efficiency.
Explanation:
All simple machines are variations of either the inclined plane or the lever. Two specific examples are the wedge, which is a simple machine consisting of two back-to-back inclined planes, and the wheel and axle, which is a simple machine consisting of a rod fixed to the center of a wheel. These machines help to multiply or augment a force, thereby providing a mechanical advantage to the user.
A complex machine, such as a bicycle or a car, combines several simple machines to perform a task more efficiently. The wire cutters, for instance, combine two levers and two wedges, while bicycles include components like wheel and axles and pulleys. The concept of mechanical advantage (MA) is crucial as it represents the ratio of output to input forces, allowing for a smaller force to perform a given task thanks to the simple machine.
Suppose the stone is thrown at an angle of 39.0° below the horizontal from the same building as in the Example above. If it strikes the ground 47.8 m away, find the following. (Hint: For part (a), use the equation for the x-displacement to eliminate v0t from the equation for the y-displacement.)
(a) the time of flight
s
The x coordinate as a function of time is x(t) = vcos(39.0)t, so the initial speed is v0 = Δx/(cos 39.0Δt), where Δx = 47.8 and Δt is the time of flight. Insert this into your equation for y(t) and solve for the time of flight.
Here are three displacements, each in meters: d1 = 1.5i + 1.8j - 5.0k, d2 = -1.0i + 2.0j + 3.0k, and d3 = 4.0i + 3.0j + 2.0k. What is r = d1 - d2 + d3 ((a), (b) and (c) for i, j and k components respectively)? (d) What is the angle between r and the positive z axis? (e) What is the component of d1 along the direction of d2? (f) What is the component of d1 that is perpendicular to the direction of d2 and in the plane of d1 and d2? ...?
The question involves adding and subtracting the vector components of three displacements and calculating the angle between the resultant vector and the z-axis. Further, it asks for the components of one displacement vector along and perpendicular to the direction of another displacement vector. These operations involve vector dot product and cross-product calculations.
Explanation:To solve this problem, you first need to subtract and add the respective i, j, and k components of the three displacements: d1, d2, and d3. Calculations will give you r which is represented by three values (a), (b), and (c) for i, j, and k components respectively.
To find the angle (d) between r and the positive z-axis, you will have to use the dot product formula and the arccos function. The component of d1 along the direction of d2 can be calculated using the dot product of d1 and the unit vector in the direction of d2 (part (e) of your question). The component of d1 perpendicular to the direction of d2 and in the plane of d1 and d2, asked in part (f), can be found using vector cross-product operations and the magnitude of the resulting vector.
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The displacement vector r is (4.5i + 2.8j - 0.9k). The angle between r and the positive z-axis is approximately 16.35°. The component of d1 along the direction of d2 is -1.5 and the component of d1 perpendicular to the direction of d2 and in the plane of d1 and d2 is (3.0i + 1.8j - 5.0k).
Explanation:The displacement vector r can be calculated by subtracting d2 from d1 and adding d3. In component form, r = (d1 - d2 + d3) = (1.5 - (-1.0) + 4.0)i + (1.8 - 2.0 + 3.0)j + (-5.0 + 3.0 + 2.0)k = 4.5i + 2.8j - 0.9k.
(d) To find the angle between r and the positive z-axis, we can calculate the dot product of r and the unit vector along the positive z-axis. The dot product is given by cos(θ) = (r dot k) / (|r||k|), where r dot k is the dot product of r and k. Since |k| = 1, we have cos(θ) = (r dot k) / |r|. Evaluating the dot product, we get the angle θ ≈ 16.35°.
(e) The component of d1 along the direction of d2 can be found using the dot product formula. The component is given by |d1| cos(θ), where θ is the angle between d1 and d2. Since θ = 180°, the component is 1.5 cos(180°) = -1.5.
(f) The component of d1 that is perpendicular to the direction of d2 and in the plane of d1 and d2 can be found by subtracting the component in the direction of d2 from d1. The component is given by d1 - (|d1| cos(θ)) = 1.5i + 1.8j - 5.0k - (-1.5i) = 3.0i + 1.8j - 5.0k.
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A snowmobile has an initial velocity of 4.7 m/s.
If it accelerates at the rate of 0.73 m/s2 for 5.6s, what is the final velocity? Answer in units of m/s, If instead it accelerates at the rate of -0.51 m/s2, how long will it take to reach a complete stop? Answer in units of s ...?
The final velocity of the snowmobile after accelerating for 5.6 seconds is approximately 8.788 m/s. If it decelerates at a rate of -0.51 m/s^2, it will take roughly 9.22 seconds to reach a complete stop.
Explanation:To find the final velocity of the snowmobile that has an initial velocity of 4.7 m/s and accelerates at the rate of 0.73 m/s2 for 5.6s, we can use the formula:
v = u + at
Where:
Plugging in the values gives us:
v = 4.7 m/s + (0.73 m/s2)(5.6 s)
v = 4.7 m/s + 4.088 m/s
v ≈ 8.788 m/s
To calculate the time it takes to reach a complete stop when the snowmobile decelerates at a rate of -0.51 m/s2, we rearrange the formula to solve for time:
t = (v - u) / a
Since the final velocity v at a complete stop is 0 m/s, the initial velocity u is 4.7 m/s (the velocity before deceleration), and a is -0.51 m/s2, the time t is:
t = (0 m/s - 4.7 m/s) / -0.51 m/s2
t ≈ 9.22 s
Will an object with a density of 1.05 g/ml float or sink in water? Explain
During a workout at the gym, you set the treadmill at a pase of 55.0 m/min. How many minutes will you walk if you cover a distance of 7500 ft? ...?
Answer:
t = 41.56 min
Explanation:
As we know that the distance moved on the trade mill is given as
[tex]d = 7500 ft[/tex]
here we know that
[tex]1 ft = 12 inch[/tex]
[tex]1 inch = 2.54 cm[/tex]
so we have
[tex]1 ft = 12 \times 2.54 cm[/tex]
[tex]1 ft = 0.3048 m[/tex]
now we know that
[tex]d = 7500 \times 0.3048 m[/tex]
[tex]d = 2286 m[/tex]
now we know that the speed on the trade mill is given as
[tex]v = 55 m/min[/tex]
so time taken to move the given distance is
[tex]t = \frac{d}{v}[/tex]
[tex]t = \frac{2286}{55}[/tex]
[tex]t = 41.56 min[/tex]