A student throws a 0.1 kg dart at an angle of 20° to the horizon. Then the student changes the throwing angle. Which angle
will maximize the distance the dart will travel before it returns to its original height?
Answer:
The student must change the launch angle from 20º to 45º to maximize the horizontal distance.
Explanation:
The dart experiments a parabolical motion, which is the combination of horizontal uniform motion and vertical uniform accelerated motion due to gravity, in which effects from air friction and Earth's rotation can be neglected. The equations of motion are described below:
[tex]x = x_{o}+v_{o}\cdot t \cdot \cos \theta[/tex] (1)
[tex]y = y_{o}+v_{o}\cdot t\cdot \sin \theta +\frac{1}{2}\cdot g\cdot t^{2}[/tex] (2)
Where:
[tex]x_{o}[/tex], [tex]y_{o}[/tex] - Initial coordinates of the dart, measured in meters.
[tex]x[/tex], [tex]y[/tex] - Current coordinates of the dart, measured in meters.
[tex]v_{o}[/tex] - Initial velocity of the dart, measured in meters per second.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]t[/tex] - Time, measured in seconds.
[tex]\theta[/tex] - Launch angle, measured in sexagesimal degrees.
According to the statement, we need to determine the launch angle when [tex]\Delta x = x-x_{o} > 0[/tex], [tex]\Delta y = y-y_{o}= 0[/tex] and [tex]v_{o} > 0[/tex]. Then, we obtain the following system of linear equations:
[tex]\Delta x = v_{o}\cdot t \cdot \cos \theta[/tex] (1b)
[tex]v_{o}\cdot \sin \theta + \frac{1}{2}\cdot g \cdot t = 0[/tex] (2b)
By (2b), we clear time as follows:
[tex]t = -\frac{2\cdot v_{o}\cdot \sin \theta}{g}[/tex]
And it is applied in (1b) afterwards:
[tex]\Delta x = -\frac{2\cdot v_{o}^{2}\cdot \sin\theta \cdot \cos\theta}{g}[/tex]
[tex]\Delta x = -\frac{v_{o}^{2}\cdot \sin 2\theta}{g}[/tex] (3)
Where [tex]\Delta x[/tex] is the horizontal distance, measured in meters.
In order to determine the launch angle such that distance is maximized, we require the first and second derivatives of the function. That is:
First derivative
[tex]\Delta x' = -\frac{2\cdot v_{o}^{2}\cdot \cos 2\theta}{g}[/tex] (4)
Second derivative
[tex]\Delta x'' = \frac{2\cdot v_{o}^{2}\cdot \sin 2\theta}{g}[/tex] (5)
By equalizing (4) to zero, we find the following trigonometric equivalence:
[tex]\cos 2\theta = 0[/tex]
[tex]2\cdot \theta = 90^{\circ}[/tex]
[tex]\theta = 45^{\circ}[/tex]
A launch angle of 45º is a critical point of (3). If we know that [tex]g< 0[/tex] and [tex]\theta = 45^{\circ}[/tex] in (5), then [tex]\Delta x'' < 0[/tex], which means that critical point determined above leads to a maximum distance. Then, the student must change the launch angle from 20º to 45º to maximize the horizontal distance.
Approximately how many Sun's are in the Milky way?
Answer:
there are uncountable sun are there but sun is star therefore there are uncountable stars are there
Answer:
1 but For many years scientists have studied our own solar system. But until the last few years, we knew of no other solar systems. This may seem surprising, as the Sun is one of about 200 billion stars (or perhaps more) just in the Milky Way galaxy alone.
Explanation:
Which way will the object accelerate if the forces given are the following
FORCE 1
FORCE 2
24 N 30 N
15 N 15 N
45 N 25 N
80 N 67 N
56 N 47 N
Explanation:
the world of introductory physics, Newton's second law is one of the most important laws you'll learn. It's used in almost every chapter of every physics textbook, so it's important to master this law as soon as possible.
We know objects can only accelerate if there are forces on the object. Newton's second law tells us exactly how much an object will accelerate for a given net force.
\Large a=\dfrac{\Sigma F}{m}a=
m
ΣF
Look at the equation below. What does the u represent?
Answer:
but you didn't give the equation the question is incomplete
Answer:
Initial velocity
Explanation:
A box with a mass of 5.8 kg is lifted from the garage floor and placed on a shelf. If the box gains 145 J of
potential energy, how high is the self?
Answer:
2.27
Explanation:
Potential energy =mgh so from there u can substitute the values
Write the expression for the frequency of a mass m on a spring moving horizontally. Suppose that k is the spring constant. Express your answer in terms of some or all of the variables k, m, g.
Answer:
[tex]f=1/2\pi *\sqrt{k/m}[/tex]
Explanation:
This is the equation of the frequency of a spring in the horizontal direction.
1. How much work does the human heart do if it uses 180 N of force to pump blood 0.3 meters to the
lungs?
Work does the human heart do if it uses 180 N of force to pump blood 0.3 meters to the lungs 39 joule.
What is work?Work in physics is the energy that is transferred to or from an item when a force is applied along a displacement. In its simplest form, it equals the product of the force's magnitude and the distance travelled for a constant force directed in the direction of motion.
Work = force x distance. In units, Joules = Newtons x meters.
W = F.d
F = 180 N d=0.3 m
W = F.d
W = (180)(0.3)
W = 39 j
Work does the human heart do if it uses 180 N of force to pump blood 0.3 meters to the lungs 39 joule.
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The velocity of a passenger relative to a boat is -vpb. The velocity of the boat relative to the river it is moving on is vbr. The velocity of the river to the shore is vrs. What is the velocity of the passenger relative to the shore
Answer:
vps = vbr + vrs - vpb
Explanation:
If the passenger were at rest, his speed relative to the shore will be identical to the boat's, as follows:vps = vbr + vrsAs he is moving in a direction opposite to the boat's, his velocity relative to the shore must be less than if he were at rest, in the same quantity that he was moving opposite to the boat, as follows:vps = vbr+ vrs -vpbA 6.0-kg object moving at 5.0 m/s collides with and sticks to a 2.0-kg object. After the collision the composite object is moving at 2.0 m/s in a direction opposite to the initial direction of motion of the 6.0-kg object. Determine the speed of the 2.0-kg object before the collision. a. 23 m/s b. 15 m/s c. 11 m/s d. 8.0 m/s e. 7.0 m/s
Answer:
a) 23 m/s
Explanation:
Assuming no external forces acting during the collision, total momentum must be conserved, as follows:[tex]p_{o} = p_{f} (1)[/tex]
The initial momentum p₀, can be written as follows:[tex]p_{o} = m_{1} * v_{1o} + m_{2}* v_{2o} = 6.0 kg * 5.0 m/s + 2.0 kg * v_{2o} (2)[/tex]
The final momentum pf, can be written as follows:[tex]p_{f} = (m_{1} + m_{2} )* v_{f} = 8.0 kg* (-2.0 m/s) (3)[/tex]
Since (2) and (3) are equal each other, we can solve for the only unknown that remains, v₂₀, as follows:[tex]v_{2o} = \frac{-6.0kg* 5m/s -8.0 kg*2.0m/s}{2.0kg} = \frac{-46kg*m/s}{2.0kg} = -23.0 m/s (4)[/tex]
This means that the 2.0-kg object was moving at 23 m/s in a direction opposite to the 6.0-kg object, so its initial speed, before the collision, was 23.0 m/s.The speed of the 2.0-kg object before the collision will be 23 m/s.Option A is correct.
What is the law of conservation of momentum?According to the law of conservation of momentum, the momentum of the body before the collision is always equal to the momentum of the body after the collision.
The given data in the problem is;
m₁ is the mass of objthe ct = 6.0-kg
v₁ is the speed moving = 5
m₂ is the mass of object 2 = 2.0 Kg
V is the final speed = 2.0 m/s
v₂ is the speed of the 2.0-kg object before the collision =?
According to the law of conservation of momentum;
Momentum before collision =Momentum after collision
[tex]\rm m_1v_1 + m_2v_2 = V(m_1 + m_2)\\\\(6 \times 5) + (2 \times v_2) = -2.0 \times (8) \\\\ \rm v_2 = \frac{-46}{2.0} \\\\ \rm v_2 =-23.0\ m/sec[/tex]
Hence the speed of the 2.0-kg object before the collision will be 23 m/s.Option A is correct.
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A child on roller skates undergoes as acceleration of 0.6m/s^2 due to a horizontal net force of 24N . What is the mass of the child?
Answer:
40Kg
Explanation:
F=m×a
24N÷0.6m/s^2=40
Which of the following is true if you stub (hit) your toe on a stone step?
Could we have the choices? If we have those we could help you! εїз
this is for physics, i need help fast!!
how is atmospheric and water pressure different?
Answer: Electric charges
Explanation: Atmospheric pressure isn't able to crush you because it doesn't result from weight or surface area. Atmospheric pressure, also known as weather patterns, results from escaping atmospheric gases coming together and creating electric charges. Oceanic pressure in caused from high compression of the upper layers of the water, producing thousands of tons of liquid weight crushing the bottom layer. This is how they are different forms of pressure.
A yo‑yo with a mass of 0.0800 kg and a rolling radius of =2.70 cm rolls down a string with a linear acceleration of 5.70 m/s2.
Calculate the tension magnitude in the string and the angular acceleration magnitude of the yo‑yo. What is the moment of inertia of this yo‑yo?
I ended up calculating the angular acceleration to be 211.11 but I'm unsure how to calculate the other parts of the problem.
Explanation:
Given that,
Mass, m = 0.08 kg
Radius of the path, r = 2.7 cm = 0.027 m
The linear acceleration of a yo-yo, a = 5.7 m/s²
We need to find the tension magnitude in the string and the angular acceleration magnitude of the yo‑yo.
(a) Tension :
The net force acting on the string is :
ma=mg-T
T=m(g-a)
Putting all the values,
T = 0.08(9.8-5.7)
= 0.328 N
(b) Angular acceleration,
The relation between the angular and linear acceleration is given by :
[tex]\alpha =\dfrac{a}{r}\\\\\alpha =\dfrac{5.7}{0.027}\\\\=211.12\ m/s^2[/tex]
(c) Moment of inertia :
The net torque acting on it is, [tex]\tau=I\alpha[/tex], I is the moment of inertia
Also, [tex]\tau=Fr[/tex]
So,
[tex]I\alpha =Fr\\\\I=\dfrac{Fr}{\alpha }\\\\I=\dfrac{0.328\times 0.027}{211.12}\\\\=4.19\times 10^{-5}\ kg-m^2[/tex]
Hence, this is the required solution.
If 400 N of force was applied to a rock and it had an acceleration of 20 ms2 , what is the mass of rock?
Answer:
20 kgExplanation:
The mass of the rock can be found by using the formula
[tex]m = \frac{f}{a} \\ [/tex]
f is the force
a is the acceleration
From the question we have
[tex]m = \frac{400}{20} = \frac{40}{2} \\ [/tex]
We have the final answer as
20 kgHope this helps you
The loudness of a sound is the waves amplitude
True or false
Answer:
true i think
Explanation:
The amplitude of a sound wave determines its loudness or volume. A larger amplitude means a louder sound, and a smaller amplitude means a softer sound. In Figure 10.2 sound C is louder than sound B. The vibration of a source sets the amplitude of a wave.
Answer:
True
Explanation:
Look up the definition of amplitude
What are the sources of error in photoelectric effect experiment?
Answer:
In this experiment the major sources of error were due many different factors, some of which included: restraints on the Voltage sensor, restraints on the actual apparatus, and faulty averages of the stopping potential.
Explanation:
The main sources of error in this experiment were caused by a variety of variables, including restrictions on the Voltage sensor, restrictions on the actual device, and inaccurate averages of the stopping potential.
What is the Photoelectric effect?When a substance absorbs electromagnetic radiation, a phenomenon known as the photoelectric effect causes electrically charged particles to be discharged from or within the material. When light strikes a metal plate, the action is frequently described as the ejection of electrons from the plate. In a more general definition, the substance may be solid, liquid, or gas, the radiant energy may take the form of infrared, visible, or ultraviolet light, X-rays, or gamma rays, and the discharged particles may include ions (electrically charged atoms or molecules) in addition to electrons.
Because of the perplexing concerns, it presented about the nature of light—particle versus wavelike behavior—that were finally answered by Albert Einstein in 1905, the phenomenon was critically important in the development of modern physics.
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Which region is located between 60-90N and 60-90S?
Group of answer choices
Tropics
Tropical Rainforest
Polar
Mid-Lats
Answer:
Polar
Explanation:
Took the test
A 20-Kg child is on a swing attached to 3.0 m-long chains. The child swings back and forth, swinging out to a 60-degree angle. (This is the angle that the chains make with the vertical.) What is the childs maximum speed on the swing
Answer:
v = 29.4 m / s
Explanation:
For this exercise we can use the conservation of mechanical energy
Lowest starting point.
Em₀ = K = ½ m v²
final point. Higher
[tex]Em_{f}[/tex] = U = m g h
Let's use trigonometry to lock her up
cos 60 = y / L
y = L cos 60
Height is the initial length minus the length at the maximum angle
h = L - L cos 60
h = L (1- cos 60)
energy is conserved
Em₀ = Em_{f}
½ m v² = mgL (1 - cos 60)
v = 2g L (1- cos 60)
let's calculate
v² = 2 9.8 3.0 (1- cos 60)
v = 29.4 m / s
Calculate how much energy (in Joules) it takes for a bird of 134.6 g to fly 34.8 m to the top of a tree from the ground. Calculate the value assuming only vertical displacement. Recall the gravitational constant is 9.81 m/s2.
Answer:
45.51 J
Explanation:
Energy in relation to vertical displacement = P.E.
P.E. (potential energy) = mgh
m = 134.6g = 0.1346 kg
g = 9.81m/s²
h = 34.8m
since, P.E = mgh = 0.1346 × 9.81 × 34.8
= 45.51J
How do forces affect the motion of an object?
Unbalanced forces acting on an object can change that object's speed, direction or both.
Balanced forces acting on an object can change that object's speed, direction or both.
Balanced forces cause objects to accelerate.
Vectors pull objects in directions
Explanation:
Unbalanced Forces in Action
Unbalanced forces can change the motion of an object in two ways. ... Second, when unbalanced forces act on a moving object, the velocity of the object will change. Remember that a change in velocity means a change in speed, direction or both speed and direction.
How does the formation of ice in the freezing compartment of a
refrigerator demonstrate the particulate nature of matter?
A. As the particle energy of matter decreases, the motion of the atoms in a
given space decreases
B. As the particle energy of matter decreases, the motion of atoms in a given
space increases
C. As the particle energy of matter increases, the motion of atoms in a given
space decreases
D. As the particle energy of matter increases, the motion of atoms remains
unchanged
Answer:
The correct option is A
Explanation:
Generally, when the temperature of matter is low and starts to cool, the kinetic energy of it's particles decreases which causes the motion of the atoms within it's particles to also decrease. When the kinetic energy of the particles decreases, it causes the matter to form a mass by coming together since it's atoms will no longer be able to move freely as before (just like in solids) - this is the reason for the formation of ice in the freezing compartment.
From the explanation above, it can be deduced that the correct option is A
What amount of heat is absorbed by 257 g of water heated from 18° C to 63° C? The specific heat of water is 4.18 J/g°C.
Answer:
Q = 48341.7 Joules.
Explanation:
Given the following data;
Mass, m = 257g
Initial temperature, T1 = 18°C
Final temperature, T2 = 63°C
Specific heat capacity of water, c = 4.18 J/g°C.
*To find the quantity of heat absorbed*
Heat capacity is given by the formula;
[tex] Q = mcdt[/tex]
Where;
Q represents the heat capacity or quantity of heat. m represents the mass of an object. c represents the specific heat capacity of water. dt represents the change in temperature.dt = T2 - T1
dt = 63 - 18
dt = 45°C
Substituting the values into the equation, we have;
[tex] Q = 257*4.18*45[/tex]
Q = 48341.7 Joules.
Therefore, the amount of heat absorbed is 48341.7 Joules.
if 49 jules of work is done when a 7 newton wagon of cheeseburgers is pulled, how far does it move?
What are the elements needed for effective teamwork?
Answer:
The five elements of successful teamwork
-Communication: Effective communication is the most important part of teamwork and involves consistently updating each person and never assuming that everyone has the same information. ...
-Delegation: Teams that work well together understand the strengths and weaknesses of each team member. ...
-Efficiency: ...
-Ideas: ...
-Support:
What would be Kelley's weight be in newtons if her mass was 70 kilograms
Answer:
Kelly's weight would be 688.47 Newtons.
Explanation:
1 Kilogram would be 9.81 Newtons.
It all depends on where Kelley is at the moment.
-- If she's on Mars, she weighs 229 N.
-- If she's on the Moon, she weighs 113N.
-- If she's on Earth, she weighs 686 N.
-- If she's in a space capsule coasting from one body to another, then there's no instrument that can measure any weight of her.
So it completely depends on where she happens to be at the moment.
What principle of fitness means that if you stop exercising your fitness level will decrease?
A.
Reversibility
B.
Overload
C.
Specificity
D.
Individuality
Answer:
A. Reversibility
Explanation:
Because if you don't progress then you do the opposite, you reverse.
Sorry if my explanation is confusing it made sense in my head i just didn't know how to put it.
hope this help. ;)
Answer:
A. Reversibility
Explanation:
A force of 29.4 N is required to pull a 100 kg ice block at constant speed along an ice surface. Find the coefficient of kinetic friction for ice on ice.
Answer:
The value is [tex]\mu_k = 0.03[/tex]
Explanation:
From the question we are told that
The force applied on the ice is [tex]F = 29.4 N[/tex]
The mass of the ice block is [tex]m = 100 \ kg[/tex]
Generally for the ice block to move at constant speed , the force applied on it must be equal to the kinetic frictional force which is mathematically represented as
[tex]F_F = m* g * \mu_k[/tex]
=> [tex]F = F_F = m* g * \mu_k[/tex]
=> [tex]29.4 = 100 * 9.8 * \mu_k[/tex]
=> [tex]\mu_k = 0.03[/tex]
Make a rule: How does the energy needed to move an electron to a higher energy level compare to the energy emitted when the electron moves back to the lower energy level
Answer:
Explanation:
Generally, the energy required to move an electron from one energy level to another energy level is referred to as quantum energy. An atom will absorb energy when it's electron(s) move from a lower energy level (ground state) to a higher energy level (excited state) and will emit energy when it's electron(s) move from a higher energy level to a lower energy level.
Since, electrons do not stay in the excited state forever, they indeed prefer the ground state and thus will always return to the ground state. When an electron thus return to the ground state, it sheds off the excess energy that took it to the excited state thus it can be said that more energy is required to take an electron to it's excited state.
Answer:
Explanation:
When an atom absorbs energy it will go up x number levels. When it admits energy it will go down to its previous energy level and emit the same exact amount of energy that was absorbed.
An object with a mass of 14 kg experiences a force of 12 N. What is the acceleration of the object? Help, please!! <3
Answer:
6/7 kg
Explanation:
We are given:
Mass of the object (m) = 14 kg
Force applied (F) = 12 N
Acceleration of the Object:
From newton's second law of motion, we know that:
F = ma
Replacing the variable with the given values
12 = 14 * m
m = 12 / 14 [dividing both sides by 14]
m = 6/7 kg
Hence, the Object has a mass of 6/7 kg