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
An archer defending a castle is on an 15.5 m high wall. He shoots an arrow straight down at 22.8 m/s. How much time does it take
kodGreya [7K]

Answer:

  about 602 milliseconds

Explanation:

The motion can be approximated by the equation ...

  y = -4.9t^2 -22.8t +15.5

where t is the time since the arrow was released, and y is the distance above the ground.

When y=0, the arrow has hit the ground.

Using the quadratic formula, we find ...

  t = (-(-22.8) ± √((-22.8)^2 -4(-4.9)(15.5)))/(2(-4.9))

  = (22.8 ± √823.64)/(-9.8)

The positive solution is ...

  t ≈ 0.60195193

It takes about 602 milliseconds for the arrow to reach the ground.

8 0
3 years ago
A certain wave has a wavelength of 35 meters and a frequency of 4.0hz. What is the speed of the wave
defon
The speed of the wave is 140
3 0
3 years ago
Planet X is a terrestrial planet in our solar system. It has 21% oxygen in its atmosphere. Humans can walk on this planet withou
Ulleksa [173]

Answer:

a planet the is human habitable or just plain out earth

Explanation:

8 0
3 years ago
Read 2 more answers
When bitten by an animal, one should:
Scrat [10]

Answer:

consider rabies injections if the animal is not found

hope it helps

4 0
2 years ago
Read 2 more answers
Explain why water, with its high specific heat capacity, is utilized for heating systems such as hot-water radiators.
Lubov Fominskaja [6]

Answer:

Answer in explanation

Explanation:

Water is mainly used as coolant in heating systems like hot-water radiators. The main function of water in such systems, is to absorb as much heat as possible, in order to decrease the temperature of the system and as a result cool it.

The specific heat capacity is the measure of heat energy that is required to raise the temperature of unit mass of a substance through 1 °C. In other words, specific heat capacity quantifies the amount of heat that can be stored by a unit mass of a substance having a degree rise in temperature.

Thus, the more specific heat a substance has, the more heat it can absorb from the hot system. Hence, the specific heat capacity of a coolant must be high.

<u>This is the reason why water, with its high specific heat capacity, is utilized for heating systems, such as radiators.</u>

5 0
3 years ago
Other questions:
  • At what distance is the electrostatic force between two protons equal to the weight of one proton?
    10·1 answer
  • How to find volume metric
    5·1 answer
  • If all this energy is added to 50 kg of water (the amount of water in a 165-lb person) at 37 ∘C, what is the final state of the
    14·1 answer
  • The following diagrams show five pairs of asteroids, labeled with their relative masses (M) and distances (d) between them. For
    6·1 answer
  • Post Test: Force Fields
    13·1 answer
  • suppose it takes 500 years to form 2 cm of new soil without erosion. Of a farmer need at least 35 cm of soil to plant a particul
    8·1 answer
  • A object of mass 33 is dropped from a height of 85 meters. Calculate the average power developed by the object in falling throug
    9·1 answer
  • A power supply has an open-circuit voltage of 40.0 V and an internal resistance of 2.00 V. It is used to charge two storage batt
    15·1 answer
  • A train travels 100 km east and then 75 km west. What is the magnitude of<br> its displacement?
    5·1 answer
  • Integrated Science- 8th grade science
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!