1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alla [95]
2 years ago
10

A projectile is launched with an initial speed of 40 mys from the foor of a tunnel whose height is 30 m. What angle of elevation

should be used to achieve the maximum possible horizontal range of the projectile?
Physics
1 answer:
KiRa [710]2 years ago
7 0

Answer:

We are given the trajectory of a projectile:

y=H+xtan(θ)−g2u2x2(1+tan2(θ)),

where H is the initial height, g is the (positive) gravitational constant and u is the initial speed. Since we are looking for the maximum range we set y=0 (i.e. the projectile is on the ground). If we let L=u2/g, then

H+xtan(θ)−12Lx2(1+tan2(θ))=0

Differentiate both sides with respect to θ.

dxdθtan(θ)+xsec2(θ)−[1Lxdxdθ(1+tan2(θ))+12Lx2(2tan(θ)sec2(θ))]=0

Solving for dxdθ yields

dxdθ=xsec2(θ)[xLtan(θ)−1]tan(θ)−xL(1+tan2(θ))

This derivative is 0 when tan(θ)=Lx and hence this corresponds to a critical number θ for the range of the projectile. We should now show that the x value it corresponds to is a maximum, but I'll just assume that's the case. It pretty obvious in the setting of the problem. Finally, we replace tan(θ) with Lx in the second equation from the top and solve for x.

H+L−12Lx2−L2=0.

This leads immediately to x=L2+2LH−−−−−−−−√. The angle θ can now be found easily.

You might be interested in
A group of atoms with aligned magnetic poles are known as which of the following?
cestrela7 [59]
A magnetic domain is a group of atoms aligns with magnetic poles. Domains are usually <span>light and dark stripes visible within each grain.</span>
4 0
3 years ago
Read 2 more answers
A sample of carbon dioxide (C°p,m = 37.11 J K−1 mol−1) of mass 2.80 g at 27°C is allowed to expand reversibly and adiabatically
My name is Ann [436]

Answer:

182 to 3 s.f

Explanation:

Workdone for an adiabatic process is given as

W = K(V₂¹⁻ʸ - V₁¹⁻ʸ)/(1 - γ)

where γ = ratio of specific heats. For carbon dioxide, γ = 1.28

For an adiabatic process

P₁V₁ʸ = P₂V₂ʸ = K

K = P₁V₁ʸ

We need to calculate the P₁ using ideal gas equation

P₁V₁ = mRT₁

P₁ = (mRT₁/V₁)

m = 2.80 g = 0.0028 kg

R = 188.92 J/kg.K

T₁ = 27°C = 300 K

V₁ = 500 cm³ = 0.0005 m³

P₁ = (0.0028)(188.92)(300)/0.0005

P₁ = 317385.6 Pa

K = P₁V₁¹•²⁸ = (317385.6)(0.0005¹•²⁸) = 18.89

W = K(V₂¹⁻ʸ - V₁¹⁻ʸ)/(1 - γ)

V₁ = 0.0005 m³

V₂ = 2.10 dm³ = 0.002 m³

1 - γ = 1 - 1.28 = - 0.28

W =

18.89 [(0.002)⁻⁰•²⁸ - (0.0005)⁻⁰•²⁸]/(-0.28)

W = -67.47 (5.698 - 8.4)

W = 182.3 = 182 to 3 s.f

7 0
2 years ago
Consider an ideal monatomic gas of N particles with mass m in thermal equilibrium at a temperature T. The gas is contained in a
harina [27]

Answer:

K.E.=\dfrac{3}{2}KT

Explanation:

Given that

Number of particle =N

Equilibrium temperature= T

Side of cube = L

Gravitational acceleration =g

The kinetic energy of an atom  given as

K.E.=\dfrac{3}{2}KT

Where

Equilibrium temperature= T

Boltzmann constant =K

        K =1.380649×10−23 J/K

3 0
2 years ago
A circular loop of wire with a radius of 20 cm lies in the xy plane and carries a current of 2 A, counterclockwise when viewed f
Zina [86]

To solve this problem we will apply the concept related to the magnetic dipole moment that is defined as the product between the current and the object area. In our case we have the radius so we will get the area, which would be

A=\pi r^2

A =\pi (0.2)^2

A =0.1256 m^2

Once the area is obtained, it is possible to calculate the magnetic dipole moment considering the previously given definition:

\mu=IA

\mu=2(0.1256)

\mu=0.25 A\cdot m^2

Therefore the magnetic dipole moment is 0.25A\cdot m^2

6 0
3 years ago
Which of the following statements about energy in systems are true?
oee [108]

Answer:

Laws of Thermodynamics

Energy exists in many forms, such as heat, light, chemical energy, and electrical energy. Energy is the ability to bring about change or to do work. Thermodynamics is the study of energy.

First Law of Thermodynamics: Energy can be changed from one form to another, but it cannot be created or destroyed. The total amount of energy and matter in the Universe remains constant, merely changing from one form to another. The First Law of Thermodynamics (Conservation) states that energy is always conserved, it cannot be created or destroyed. In essence, energy can be converted from one form into another. Click here for another page (developed by Dr. John Pratte, Clayton State Univ., GA) covering thermodynamics.

The Second Law of Thermodynamics states that "in all energy exchanges, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state." This is also commonly referred to as entropy. A watchspring-driven watch will run until the potential energy in the spring is converted, and not again until energy is reapplied to the spring to rewind it. A car that has run out of gas will not run again until you walk 10 miles to a gas station and refuel the car. Once the potential energy locked in carbohydrates is converted into kinetic energy (energy in use or motion), the organism will get no more until energy is input again. In the process of energy transfer, some energy will dissipate as heat. Entropy is a measure of disorder: cells are NOT disordered and so have low entropy. The flow of energy maintains order and life. Entropy wins when organisms cease to take in energy and die.

Potential vs. Kinetic energy

Potential energy, as the name implies, is energy that has not yet been used, thus the term potential. Kinetic energy is energy in use (or motion). A tank of gasoline has a certain potential energy that is converted into kinetic energy by the engine. When the potential is used up, you're outta gas! Batteries, when new or recharged, have a certain potential. When placed into a tape recorder and played at loud volume (the only settings for such things), the potential in the batteries is transformed into kinetic energy to drive the speakers. When the potential energy is all used up, the batteries are dead. In the case of rechargeable batteries, their potential is reelevated or restored.

In the hydrologic cycle, the sun is the ultimate source of energy, evaporating water (in a fashion raising it's potential above water in the ocean). When the water falls as rain (or snow) it begins to run downhill toward sea-level. As the water get closer to sea-level, it's potential energy is decreased. Without the sun, the water would eventually still reach sea-level, but never be evaporated to recharge the cycle.

Chemicals may also be considered from a potential energy or kinetic energy standpoint. One pound of sugar has a certain potential energy. If that pound of sugar is burned the energy is released all at once. The energy released is kinetic energy (heat). So much is released that organisms would burn up if all the energy was released at once. Organisms must release the energy a little bit at a time.

Energy is defined as the ability to do work. Cells convert potential energy, usually in the from of C-C covalent bonds or ATP molecules, into kinetic energy to accomplish cell division, growth, biosynthesis, and active transport, among other things.

Learning Objectives 

These learning objectives are taken from my Biology for Nonmajors class (BIO 102). I have tried to add a link to each that will direct you to a part of this chapter or another website that will facilitate your completion of the objective.

Define energy; be able to state the first and second laws of thermodynamics.

Entropy is a measure of the degree of randomness or disorder of systems. Explain how life maintains a high degree of organization.

8 0
3 years ago
Other questions:
  • A rubber balloon has become negatively charged from being rubbed with a wool cloth, and the charge is measured as 1.00 × 10−14 C
    13·1 answer
  • In general, which of the following is NOT a critical skill for participating in a sport? A. agility and balance B. endurance and
    13·2 answers
  • Which process will be MOST AFFECTED by the heat?
    5·2 answers
  • Integrated Concepts When kicking a football, the kicker rotates his leg about the hip joint. (a) If the velocity of the tip of t
    6·1 answer
  • A battery with an emf of 24.0 V is connected to a resistive load. If the terminal voltage of the battery is 16.1 V and the curre
    9·1 answer
  • Jason rides his bicycle 1,200 meters east to the grocery store. He then turns around and travels 760 meters west to meet his fri
    7·1 answer
  • What kind of small object composes much of the universe?
    14·1 answer
  • I need help on this
    11·1 answer
  • A horizontal force of 300.0 N is used to push a 145-kg mass 30.0 m horizontally in 3.00 s. Calculate the power developed.
    6·1 answer
  • HELP 30 POINTS
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!