A rider on a water slide goes through three different kinds of motion, as illustrated in the figure below. Use the data and the details from the figure to answer the following questions. Remember, when an object is in a circular motion it is accelerated toward the center of the circle with acceleration a = v2/r
a) At the end of the first section of the motion, riders are moving at approximately what speed? Show your work for partial credit.
A. 3 m/s B. 6 m/s C. 9 m/s D. 12 m/s
b) Suppose the acceleration during the second section of the motion is too large to be comfortable for the riders. What change could be made to decrease the acceleration during this section?
A. Reduce the radius of the circular segment
B. Increase the radius of the circular segment
C. Increase the angle of the ramp.
D. Increase the length f the ramp.
c) What is the vertical component of the velocity of the rider as he hits the water? Show your work for partial credit.
A. 2.4 m/s B. 3.4 m/s C. 5.2 m/s D. 9.1 m/s
d) Suppose the designers of the water slide want to adjust the height h above the water so that the riders land twice as far away from the bottom of the slide. What would be the necessary height above the water? Show your work for partial credit.
A. 1.2 m B. 1.8 m C. 2.4 m D. 3.0 m
e) During which section of the motion is the magnitude of the acceleration experienced by the rider the greatest?
A. The first B. The second C. The third D. It is the same in all sections
Answers
a) C. 9 m/s
First of all, let's calculate the difference in height between the starting point of the motion and the end point of the first section. It is given by:
[tex]\Delta h = L sin \theta[/tex]
where
L = 6.0 m
[tex]\theta=45^{\circ}[/tex]
Substituting,
[tex]\Delta h = (6.0)(sin 45^{\circ})=4.2 m[/tex]
Assuming the rider starts from rest, its initial speed is zero. For the law of conservation of energy, the decrease in gravitational potential energy of the rider will be equal to its gain in kinetic energy, so we can write:
[tex]mg\Delta h = \frac{1}{2}mv^2[/tex]
where m is the rider's mass, g = 9.8 m/s^2 is the acceleration of gravity, and v is the speed at the end of the first section. Solving for v, we find:
[tex]v=\sqrt{2g\Delta h}=\sqrt{2(9.8)(4.2)}=9.1 m/s \sim 9 m/s[/tex]
b) B. Increase the radius of the circular segment
In fact, the acceleration during the second section of the motion (circular motion) is given by the formula for the centripetal acceleration:
[tex]a=\frac{v^2}{r}[/tex]
where
v is the speed at the end of the first section
r is the radius of the circle
We notice that the acceleration is
- Proportional to the square of the speed
- Inversely proportional to the radius
So, we immediately see that if we increase the radius of the circle (choice B), the acceleration will decrease.
c) B. 3.4 m/s
When the rider exits the second section of the motion, he has a speed (completely horizontal) of 9.1 m/s (calculated in part (a); it didn't change, because the speed during the second section does not change).
The vertical component of his velocity is instead zero, since his motion is completely horizontal. Therefore, we can use the following SUVAT equation along the vertical direction:
[tex]v_y^2 - u_y^2 = 2g\Delta h[/tex]
where
[tex]v_y[/tex] is the vertical component of the velocity as the rider hits the water
[tex]u_y=0[/tex] is the vertical component of the velocity as the rider starts the 3rd section
[tex]\Delta h = 0.60 m[/tex] is the difference in height
Solving for [tex]v_y[/tex],
[tex]v_y = \sqrt{2g\Delta h}=\sqrt{2(9.8)(0.60)}=3.4 m/s[/tex]
d) C. 2.4 m
We want here the rider to land twice as far compared to before.
The horizontal distance travelled by the rider in section 3 is entirely determined by his horizontal motion. The horizontal component of the velocity, which is constant, is
[tex]v_x = 9.1 m/s[/tex]
calculated at part (a) and remained unchanged during section 2. The horizontal distance travelled during section 3 is
[tex]d=v_x t[/tex] (1)
where t is the time of the fall. This can be rewritten as
[tex]t=\frac{d}{v_x}[/tex]
We also know that the vertical displacement is:
[tex]h=\frac{1}{2}gt^2[/tex]
Substituting t from (1) into this equation, we find
[tex]h=\frac{gd^2}{2v_x^2}[/tex]
So we see that the height needed is proportional to the square of the distance: [tex]h \propto d^2[/tex]. Therefore, in order to land at twice the previous distance, the height must be 4 times the previous one, so:
[tex]h=4 (0.6 m)=2.4 m[/tex]
e) B. The second
We need to calculate the acceleration in each section.
In section 1 (motion along the slope), it is:
[tex]a=g sin \theta = (9.8)(sin 45^{\circ})=6.9 m/s^2[/tex]
In section 2 (circular motion), the acceleration is the centripetal acceleration:
[tex]a=\frac{v^2}{r}=\frac{9.1^2}{1.5}=55.2 m/s^2[/tex]
In section 3, the motion is free fall, so the acceleration is equal to the acceleration of gravity:
[tex]a=g=9.8 m/s^2[/tex]
Therefore, the rider experiences the largest acceleration in section 2.
This answer explains how to calculate the speed, acceleration, and vertical component of velocity for a rider on a water slide, as well as how to adjust the height to change the landing distance and determine the section with the greatest acceleration.
Explanation:To answer these questions about the rider on the water slide, we need to use the formula for acceleration in circular motion, which is a = v2/r. For question a, we can use the given information to calculate the speed at the end of the first section of motion. For question b, reducing the radius of the circular segment would decrease the acceleration during the second section. For question c, we need to calculate the vertical component of the rider's velocity as he hits the water. For question d, we can use the concept of projectile motion to determine the necessary height above the water to land twice as far away. Finally, for question e, we need to determine during which section of the motion the magnitude of the acceleration experienced by the rider is the greatest.
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Related Questions
A particle starts at the origin and moves away from it in a straight line. After 1.6 seconds, it is 12.8 meters from the origin. It then reverses direction due to a force field with a like charge. After 3.8 seconds total, the particle is at −9.23 m. What is the average velocity of the particle? 3.8 m/s −5.8 m/s −2.4 m/s 13.8 m/s
Answers
Answer:
Average velocity of the particle is[tex]-2.4 m/s[/tex]
Explanation:
Average velocity is defined as the total velocity divided by the total time. It is given by the equation[tex]v_av= \frac{displacement}{(total time taken)}[/tex]
In the given problem the particle starts from origin, travels [tex]12.8 m[/tex] and then reverses direction and travels till [tex]-9.23 m[/tex] within a total time of [tex]3.8 seconds.[/tex]
Displacement is defines as the shortest distance between initial and final point.
Here displacement = [tex]- 9.23 m[/tex]
total time=[tex]3.8 s[/tex]
[tex]v_av=-9.23/3.8=-2.4 m/s[/tex]
if a particle moving in straight line such that its position varies with time as x=5(t-2) + 6(t-2)^2 ,then intial acceleration is
Answers
Answer:
12
Explanation:
x = 5 (t − 2) + 6 (t − 2)²
x = 5t − 10 + 6 (t² − 4t + 4)
x = 5t − 10 + 6t² − 24t + 24
x = 6t² − 19t + 14
Velocity is the derivative of position with respect to time:
v = dx/dt
v = 12t − 19
Acceleration is the derivative of velocity with respect to time:
a = dv/dt
a = 12
The particle's acceleration is constant at 12 (use appropriate units).
If a wave has a period of 0.077 sec, it has a frequency of
01/13 Hz.
3.6 Hz.
169 Hz.
13 Hz.
Answers
Answer: 13 Hz
Explanation:
The frequency [tex]f[/tex] of a wave is expressed as:
[tex]f=\frac{1}{T}[/tex]
Where [tex]T[/tex] is the period of the wave
If we are told the period is 0.077 s, then its frequency is:
[tex]f=\frac{1}{0.077 s}[/tex]
[tex]f=12.98 Hz \approx 13 Hz[/tex]
An elevated weighing 15,00 Newton’s is raised one story in 50 seconds. If the distance stories is 3.0 meters how much power is required of the motor
Answers
Power required for motor to raise elevated weighing 1500 newton for a distance of 3 meter in 50 second is 90 watt.
Solution:
By using power force formula,
Power is obtained by multiplying force and velocity
[tex]\text { Power }=\text { Force } \times \text { Velocity }[/tex]
Velocity can be calculated by dividing distance by time.
[tex]\begin{array}{l}{\text {Velocity}=\frac{\text {Distance}}{\text {Time}}} \\ {\text {Power}=\text {Force} \times \frac{\text {Distance}}{\text {Time}}}\end{array}[/tex]
So for a force of 1500 newton with distance 3 meter for a time period 50 second, power is given as,
[tex]\text { Power }=1500 \times \frac{3}{50}=150 \times \frac{3}{5}=30 \times 3 = 90[/tex]
Power = 90 watt
It takes a pulse of light 35 microseconds to travel down a 5.0 km length of fiber optic cable. How fast does light move through the cable (in m/s)?
Answers
for a machine, the input force is 30 N, and the input distance is 2 m. Factoring in the effect of friction, what must be true about the work output?
A. It must be greater than 60 J
B. It equals 60 J.
C. It must be less than 60 J
Answers
Answer:
C. It must be less than 60 J
Explanation:
The work going into the machine is the product of the force and distance:
W = Fd
W = (30 N) (2 m)
W = 60 J
The work out of the machine is less than this due to the frictional losses.
Answer:
C. It must be less than 60 J
A telephone wire has a current 20A flowing through it . How long does it take for a charge of 15 C to pass through the wire?
Answers
Q = It
t = Q/I = 15/20 = 0.75 s
It will take 0.75 s for a charge of 15 C to flow through the wire.
The quantity of electricity flowing through a wire is related to current and time according to the following equation:
Q = ItWhere
Q is the quantity of electricity
I is the current
t is the time
With the above formula, we can calculate the time taken for the 15 C to flow through the wire. This can be obtained as follow:
Quantity of electricity (Q) = 15 C
Current (I) = 20 A
Time (t) =?Q = It
15 = 20 × t
Divide both side by 20
[tex]t = \frac{15}{20}\\\\[/tex]
t = 0.75 sTherefore, it will take 0.75 s for a charge of 15 C to flow through the wire.
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How long did it take beagle to sail from Tahiti back to Falmouth, England?
Answers
Answer:
On 2 October 1836, the Beagle entered the English port of Falmouth after a voyage which had lasted for four years, nine months and five days.
The Beagle voyage from Tahiti to Falmouth, England took five years.
The Beagle took five years to sail from Tahiti back to Falmouth, England as part of Charles Darwin's famous voyage on the HMS Beagle from 1831 to 1836.
A man moving at 2 m/s accelerates at a rate of 3 m/s² for 2.5 seconds. What is the new velocity of the man?
Answers
Using the kinematic equation v = u + at, the man's new velocity is found to be 9.5 m/s after accelerating at 3 m/s² for 2.5 seconds.
Explanation:To calculate the new velocity of the man after accelerating, we apply the basic kinematics equation v = u + at, where:
v is the final velocity (which we are trying to find).u is the initial velocity.a is the acceleration.t is the time over which the acceleration occurs.Given that the man's initial velocity (u) is 2 m/s, acceleration (a) is 3 m/s², and the time (t) is 2.5 seconds, we substitute these values into the equation:
v = 2 m/s + (3 m/s²)(2.5 s)
This yields:
v = 2 m/s + 7.5 m/s
The new velocity of the man is:
v = 9.5 m/s
Current functional magnetic resonance imaging (fMRI) technology allows researchers to:
a. Predict the likelihood of developing Alzheimer's disease.
b. Diagnose most forms of mental illness.
c. Identify selected sentences that a person reads in a scanner.
d. Read a person's private thoughts at a distance.
Answers
fMRI technology allows researchers to analyze brain activity by tracking blood flow changes related to neural activity. It can identify selected sentences that a person reads in a scanner, but it cannot predict Alzheimer's, diagnose most mental illnesses, or read private thoughts at a distance.
Explanation:Current functional magnetic resonance imaging (fMRI) technology enables researchers to observe and analyze changes in the brain's activity over time by tracking blood flow and oxygen levels. fMRI is utilized for a variety of medical and psychological assessments. It is highly effective at mapping brain function and determining the functioning of various regions involved in thought and motor control. Specifically, fMRI can measure changes in blood flow associated with neural activity and can thereby generate a detailed map showing the most active parts of the brain during a given task.
Answering the student's multiple-choice question, among the provided options, fMRI technology can c. Identify selected sentences that a person reads in a scanner. The ability to predict the development of Alzheimer's, diagnose most forms of mental illness, or read a person's private thoughts at a distance is not explicitly achievable with the current fMRI technology.
the amount of water returning to the earth through precipitation is blank the amount of water leaving the earth through evaporation
Answers
Answer:
The amount of water entering the earth through precipitation is equal to the amount of water leaving earth through transpiration.
Explanation:
Rates of precipitation and evaporation vary widely according to regions and seasons. But in a global scale the rates are equal. Thus the total amount of earth’s water maintains its constancy even though there is a continuous change in forms of water.
Evaporation and transpiration are the forms in which Water leaves the earth and it returns to the earth in various forms of precipitation like rain, snow, dew, fog etc. This water then reaches ocean and land. The water that reaches the land flows as surface run off into rivers and water bodies or seep into the ground replenishing the ground water table.
The water cycle is a balanced system that allows water to circulate between the earth's oceans, atmosphere, and land. Water leaves the earth through evaporation/sublimation, reenters the atmosphere, condenses, and falls back to the earth through precipitation. The amount of water returning to the earth matches the amount leaving it, maintaining equilibrium.
Explanation:The water cycle, also known as the hydrological cycle, is a continuous process by which water circulates between the earth's oceans, atmosphere, and land. This cycle involves several key stages such as evaporation/sublimation, condensation/precipitation, and surface runoff/snowmelt.
Firstly, water from the land and oceans enters the atmosphere through evaporation or sublimation, where it condenses into clouds. This condensation ultimately falls back to the earth's surface as precipitation, such as rain or snow. Therefore, the amount of water returning to the earth through precipitation equals the amount of water leaving the earth through evaporation.
Once the water hits the earth, some of it may infiltrate into the soil or enter freshwater bodies. In most natural terrestrial environments, rain encounters vegetation before it reaches the soil surface. Some of this water evaporates immediately from the surfaces of plants in a process known as evapotranspiration.
After precipitation, water may travel over the surface as runoff into various bodies of water, eventually reentering the ocean, thus completing the cycle. In conclusion, the water cycle is a balanced system with the water leaving and coming back to the earth in similar quantities.
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A train moving with a velocity of 87.1 km/hour North, increases its speed with a uniform acceleration of 0.250 m/s2 North until it reaches a velocity of 160.0 km/hour North. What distance did the train travel while it was increasing its velocity, in units of meters?
Answers
Answer:
2780 meters
Explanation:
First, convert km/hr to m/s.
87.1 km/hr × (1000 m / km) × (1 hr / 3600 s) = 24.2 m/s
160.0 km/hr × (1000 m / km) × (1 hr / 3600 s) = 44.4 m/s
Given:
v₀ = 24.2 m/s
v = 44.4 m/s
a = 0.250 m/s²
Find: x
v² = v₀² + 2a (x − x₀)
(44.4 m/s)² = (24.2 m/s)² + 2(0.250 m/s²) (x − 0 m)
x = 2780 m
The net Forward force on the propeller of a 3.2 KG model airplane is 7.0 N. What is the acceleration of the airplanes
Answers
Answer:
[tex]2.1875 ms^{-2}[/tex]
Explanation:
Newton's second law: [tex]F=ma[/tex] Let's substitute and solve for whatever is left behind:[tex]7.0N= 3.2kg *a[tex]a =\frac {7.0}{3.2} \frac{N}{kg} = 2.1875 \frac{kg\frac{m}{s^2}}{kg}=2.1875 \frac{m}{s^2}[/tex]
The value of acceleration of the airplane is [tex]2.19 \;\rm m/s^{2}[/tex].
Given data:
The mass of propeller model is, m = 3.2 kg.
The net force on the propeller model is, F = 7.0 N.
Apply the Newton's second law, which says that the applied force on an object is equal to the product of mass of object and acceleration of object, caused due to applied force.
Then the expression is,
[tex]F = m \times a[/tex]
here, a is acceleration.
Solving as,
[tex]7 = 3.2 \times a\\a=2.19 \;\rm m/s^{2}[/tex]
Thus, the required value of acceleration of the propeller model is [tex]2.19 \;\rm m/s^{2}[/tex].
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a physics student drops a rock from a 55m cliff. How long does it take to hit the ground?
Answers
Answer: 9.9 seconds
Explanation:
that's just how long it takes
To hit the ground it takes approximately 3.19 seconds for the rock to hit the ground when dropped from a 55-meter cliff.
To calculate the time it takes for the rock to hit the ground when dropped from a certain height, we can use the kinematic equation for free fall:
ℎ = 1/2 gt2
Where:
h is the height of the cliff (55 m in this case).
g is the acceleration due to gravity ( 9.8 m/s2 approximately on the surface of the Earth).
t is the time we're trying to find.
Rearranging the equation to solve for t:
t =[tex]\sqrt{ 2h / g}[/tex]
Plugging in the values:
t =[tex]\sqrt{ 2(55)m / 9.8m/s²}[/tex]
Calculating this:
t≈3.19s
So, it takes approximately 3.19 seconds for the rock to hit the ground when dropped from a 55-meter cliff.
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Which fractures tend to occur first when a pane of glass is struck?
A. Radial fractures
B.
Concentric fractures
c. Spider web fractures
D. Impact fractures
Answers
Radial fractures tend to occur first when a pane of glass is struck.
Answer: Option A
Explanation:
There is a slight difference between radial and concentric fractures and as radial fractures are formed which extends outwards in a radial manner from the point where the glass is struck.
Whereas concentric fractures are circular in pattern and they terminate long before radial crack. Also when a bullet is fired from a gun, a similar reaction is observed as it gets struck on the surface and fractures are formed in the same pattern.
The Anwer is: A Radical Fractures
What is suspension?
Answers
Answer:
A suspension is essentially a damped spring producing opposing force when being compressed. ... The force produced by the dampers depend on how fast the suspension is being compressed or elongated (contact speed), opposing the movement. When a wheel is lifted from the ground the suspension produces no force.
What planet with the largest rings
Answers
Answer: saturn
Explanation:
A cat is moving at 18 m/s when it accelerates at 4 m/s2 for 2 second. what is his new velocity?
Answers
Answer: [tex]26\ \frac{m}{s}[/tex]
Explanation:
His new velocity is the "Final velocity". In order to calculate it, you need to use the following formula:
[tex]V_f=V_0+at[/tex]
Where [tex]V_f[/tex] is the Final velocity, [tex]V_0[/tex] is the Initial velocity, [tex]a[/tex] is the acceleration and [tex]t[/tex] is the time.
Based on the information provided in the exercise, you can identify that:
[tex]V_0=18\ \frac{m}{s}\\\\a=4\ \frac{m}{s^2}\\\\t=2\ s[/tex]
Therefore, you can substitute values into the formula:
[tex]V_f=18\ \frac{m}{s}+(4\ \frac{m}{s^2})(2\ s)\\\\V_f=26\ \frac{m}{s}[/tex]
Then, his new velocity is [tex]26\ \frac{m}{s}[/tex]
A central purple circle labeled N a has 3 concentric rings around it. The inner ring has 2 small green spheres. The middle ring has 8 small green spheres. The outer ring has 1 small green sphere. Does this atom satisfy the octet rule? Why or why not?
Answers
Answer:
This atom doesn’t satisfy octet rule
Explanation:
To satisfy octet rule the outermost shell should have 8 electrons. This is called octet electronic configuration which makes the atom stable. When participating in chemical reactions atoms tend to lose or gain electrons or share electrons like in a covalent bond all to achieve the octet configuration.
In this atom there are three shells and 11 electrons in total. Maximum number of electrons that can be present in the first shell is two and in this atom the first shell contains that maximum electrons. The second can contain maximum 8 electrons. In this atom the second shell is fully filled with 8 electrons.
For octet rule to be satisfied the outermost shell or the valence shell should contain 8 electrons. But in this atom the outermost shell has 1 electron. This means that the atom doesn’t satisfy octet rule. In order to obtain the octet configuration it should lose 1 electron.
Answer:
Answer
Explanation:
Sample Response: No, it does not, because the octet rule says that an atom needs to have eight electrons in its valence shell to be stable. The exceptions are hydrogen and helium, which need only two electrons. This atom has only one electron.
Traveler A starts from rest at a constant acceleration of 6 m/s^2. Two seconds later, traveler B starts with an initial velocity of 20 m/s at the same acceleration of 6 m/s^2. as measured by a, at what time will traveler B overtake traveler A?
a. 0.4s
b. 1.5s
c. 2.0s
d. 2.5s
e. 3.5s
Answers
Answer:
3. 3.5 s
Explanation:
The position of traveller A is given by the equation:
[tex]x_A(t) = \frac{1}{2}a t^2[/tex]
where
[tex]a = 6 m/s^2[/tex] is the acceleration of A
t is the time measured from when A started the motion
The position of traveller B instead is given by
[tex]x_B(t) = u_B (t-2) + \frac{1}{2}a(t-2)^2[/tex]
where a (acceleration) is the same as traveller A, and
[tex]u_B = 20 m/s[/tex]
is B's initial velocity. We can verify that the formula is correct by substituting t=2, and we get [tex]x_B=0[/tex], which means that B starts its motion 2 seconds later.
Traveller B overtakes traveller A when the two positions are the same, so:
[tex]x_A = x_B\\\frac{1}{2}at^2 = u_B (t-2) + \frac{1}{2}a(t-2)^2\\\frac{1}{2}at^2 = u_B t - 2u_B +\frac{1}{2}at^2 +2a-2at\\u_Bt-2at = 2u_B-2a\\t=\frac{2u_B-2a}{u_B-2a}=\frac{2(20)-2(6)}{20-2(6)}=3.5 s[/tex]
Although the temperature gradient changes from region to region in the homosphere, there is one gradient that stays the same. it continues to decrease as you increase in altitude, no matter where you are in the homosphere. what gradient?
please answer quick
Answers
Answer: The amount of air gradient.
Explanation:
Answer:
Pretty sure the answer is air gradient
Explanation:
In a wet cell battery what is the electrolyte?
copper
liquid acid
zinc
Answers
Answer:
the liquid acid
Explanation:
This because electrolytes are supposed to be in a liquid form.
Answer:
Liquid Acid
Explanation:
The wet cell battery implies that it has an liquid inside.
The Copper and the Zinc are also the compounts that will react in the battery as the semi-reactions implies:
Cu2+(aq) + 2e- --> Cu0
Zn2+(aq) + 2e- --> Zn0
The electrolyte is a substance present in the battery that will help the electricity to flow to the ion of interest and will not participate in the reaction, the acid should work as the electrolyte in this case.
pls help me solve this physics question
Answers
Answer:
C. 1.4 m/s
Explanation:
Energy is conserved:
Initial energy = final energy
At P, the pendulum has only gravitational potential energy.
At Q, the pendulum has only kinetic energy.
PE = KE
mgh = ½mv²
v = √(2gh)
Given h = 0.1 m:
v = √(2 × 9.8 m/s² × 0.1 m)
v = 1.4 m/s
Answer:
1.4
Explanation:
Which of the following is derived unit?
A: g (grams, mass)
B: m (meters,length)
C: s (seconds, time)
D: m2 (square meters, area)
Answers
Answer:
D: m² (square meters, area)
Explanation:
Derived units are a combination of SI base units. m² is the only option that's a combination of base units (meters times meters).
5. What happens to the arrangement of water molecules as ice melts?
A Molecules gain enough energy to escape as vapor.
B Molecules release enough energy to escape as vapor.
C Molecules gain enough energy to move from their fixed positions.
D Molecules release enough energy to move from their fixed positions.
Answers
Answer: I am pretty sure the answer is B
Explanation: If not sorry bro.
A Porsche challenges a Honda to a 500 m race
Answers
Two airplanes leave an airport at the same time. The velocity of the first airplane is 740 m/h at a heading of 25.3◦. The velocity of the second is 570 m/h at a heading of 82◦.
How far apart are they after 1.5 h? Answer in units of m.
Answers
Final answer:
The distance between the two airplanes after 1.5 hours is 255 m.
Explanation:
To find the distance between the two airplanes after 1.5 hours, we first need to determine the displacement of each airplane. Displacement is a vector quantity that represents the change in position. We can calculate the displacement of the first airplane using the equation:
Displacement = Velocity × Time
Substituting in the given values:
Displacement1 = (740 m/h) × (1.5 h) = 1110 m
Similarly, we can calculate the displacement of the second airplane:
Displacement2 = (570 m/h) × (1.5 h) = 855 m
Finally, we can find the distance between the two airplanes by subtracting the displacements:
Distance = Displacement1 - Displacement2 = 1110 m - 855 m = 255 m
Measuring spoons are used when measuring
less than how much?
Answers
Measuring spoons are used when measuring less than 1/4 cup
We can see here that measuring spoons are used when measuring less than 1/4.
What is Measuring spoon?Measuring spoons are used when measuring less than one tablespoon or teaspoon of an ingredient. These spoons are designed to provide accurate measurements for small quantities of dry or liquid ingredients used in cooking and baking. Measuring spoons typically come in sets, with the most common sizes being 1 tablespoon (tbsp), 1 teaspoon (tsp), 1/2 teaspoon, 1/4 teaspoon, and sometimes 1/8 teaspoon.
When recipes call for precise measurements of ingredients, especially in baking, measuring spoons are essential to ensure the right balance of flavors and the desired outcome of the dish. They are particularly useful when dealing with potent or costly ingredients, as small variations in quantities can significantly impact the final result.
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A ball is thrown straight up at an initial speed of 9.8m/s and, on returning to your hand, hits it moving downward at the same speed. If the whole trip took 2.0s, determine the ball’s (a) average acceleration and (b) average velocity.
Answers
Answer:
-9.8 m/s²
0 m/s
Explanation:
Average acceleration is the change in velocity over change in time.
a = Δv / Δt
a = (-9.8 m/s − 9.8 m/s) / 2.0 s
a = -9.8 m/s²
Average velocity is the change in position over change in time.
v = Δx / Δt
v = (0 m − 0 m) / 2.0 s
v = 0 m/s
In terms of Physics, the ball's average acceleration is 0 m/s² and the average velocity is also 0 m/s due to the ball returning to its initial position, making the total displacement 0.
Explanation:The subject of this question is Physics and it would be typically asked at the High School level.
(a) The ball’s average acceleration during the entire journey can be determined by the equation for motion which is: a = Δv/Δt. Here, Δv (the change in velocity) is 0 as the ball starts and ends at the same speed (it just changes direction, which is not considered in average acceleration), and Δt is the time it takes for the journey, which is 2.0 seconds. Therefore, a=0/2.0 = 0 m/s².
(b) The average velocity of an object is the total displacement (total distance travelled in a specific direction) divided by the amount of time taken to travel this distance. In this case, the ball returns to the starting point, making the total displacement 0. Therefore, the average velocity is 0/2.0 = 0 m/s.
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What happens to the force between the spheres when you increase the mass of one of the spheres?
What happens to the force between the spheres when you increase the mass of both spheres?
Answers
The force between the spheres increases when the mass increases in one of the spheres.
Explanation:
Newton law of universal gravity extends gravity beyond the earth's surface. This gravity depends directly on the mass of both objects and is inversely proportional to square of distance between their centers.
[tex]\bold{F=\frac{G \times\left(m_{1} \times m_{2}\right)}{\left(r^{2}\right)}}[/tex]
Since gravity is directly proportional to “mass of both interacting objects”, stronger objects with greater gravitational force attract. If the mass of one object increases, gravity between them also increases. For example, if an object's mass of one double, force between them also doubles.
Answer: The force between two spheres increase when mass of one or both spheres are increased.
Explanation:
According to universal law of gravitation “every body in the universe attracts every other body with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them”.
It is given by the expression
[tex]F=(GM_1 M_2)/r^2[/tex]
Where G is the gravitational constant, [tex]M_1 ,M_2[/tex] are the masses of the bodies and r is the distance between them.
In the question two conditions are given.
Mass of one object is increasedMasses of both objects are increased.Since force between two objects is directly proportional to the masses, the force increases in both cases.