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pashok25 [27]
3 years ago
14

You are working as an assistant to an air-traffic controller at the local airport, from which small airplanes take off and land.

Your job is to make sure that airplanes are not closer to each other than a minimum safe separation distance of 2.00 km. You observe two small aircraft on your radar screen, out over the ocean surface. The first is at altitude 800 m above the surface, horizontal distance 18.0 km, and 25.0° south of west. The second aircraft is at altitude 1,100 m, horizontal distance 20.0 km, and 20.0° south of west.
1. Your supervisor is concerned that the two aircraft are too close together and asks for a separation distance (in km) for the two airplanes. (Place the x-axis west, the y-axis south, and the z-axis vertical.)
Physics
1 answer:
Alika [10]3 years ago
7 0

Answer:

d = 2021.6 km

Explanation:

We can solve this distance exercise with vectors, the easiest method s to find the components of the position of each plane and then use the Pythagorean theorem to find distance between them

Airplane 1

Height   y₁ = 800m

Angle θ = 25°

           cos 25 = x / r

           sin 25 = z / r

           x₁ = r cos 20

           z₁ = r sin 25

          x₁ = 18 103 cos 25 = 16,314 103 m = 16314 m

          z₁ = 18 103 sin 25 = 7,607 103 m= 7607 m

2 plane

Height   y₂ = 1100 m

Angle θ = 20°

          x₂ = 20 103 cos 25 = 18.126 103 m = 18126 m

          z₂ = 20 103 without 25 = 8.452 103 m = 8452 m

The distance between the planes using the Pythagorean Theorem is

         d² = (x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²2

Let's calculate

        d² = (18126-16314)²  + (1100-800)² + (8452-7607)²

        d² = 3,283 106 +9 104 + 7,140 105

        d² = (328.3 + 9 + 71.40) 10⁴

        d = √(408.7 10⁴)

        d = 20,216 10² m

        d = 2021.6 km

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Flauer [41]

Explanation:

Given that,

Initial speed of the sports car, u = 80 km/h = 22.22 m/s

Final speed of the runner, v = 0

Distance covered by the sports car, d = 80 km = 80000 m

Let a is the acceleration of the sports car.  It can be calculated using third equation of motion as :

v^2-u^2=2ad

a=\dfrac{v^2-u^2}{2d}

a=\dfrac{0-(22.22)^2}{2\times 80000}

a=-0.00308\ m/s^2

Value of g, g=9.8\ m/s^2

a=\dfrac{-0.00308}{9.8}\ m/s^2

a=(-0.000314)\ g\ m/s^2

Hence, this is required solution.

8 0
3 years ago
Mercury has a radial acceleration of 3.96 × 10−2 m/s2 and its orbital period is T = 88 days. What is the radius of Mercury’s orb
Maslowich

Answer: 58,045,522,878.8 meters

Explanation:

Ok, the data we have is

Period = T = 88 days

Radial acceleration = ar = 3.96x10^-2 m/s^2

And we know that the equation for the radial acceleration is:

ar = v^2/r = r*w^2

Where v is the velocity. r is the radius and w is the angular velocity.

And we know that:

w = 2*pi*f

where f is the frequency, and:

T = 1/f.

Then we can write:

w = 2*pi/T

and our equation becomes:

ar = r*(2*pi/T)^2

Now we solve this for r.

First we need to use the same units in both equations, so we want to write T in seconds.

T = 88 days,

A day has 24 hours, and one hour has 3600 seconds:

T = 88*24*3600 s =7,603,200s

Then:

3.96x10^-2 m/s^2 = r*(2*3.14/7,603,200s)^2

r = (3.96x10^-2 m/s^2) /(2*3.14/7,603,200s)^2 = 58,045,522,878.8 meters

5 0
3 years ago
A skier (m=59.0 kg) starts sliding down from the top of a ski jump with negligible friction and takes off horizontally. If h = 3
marissa [1.9K]

Answer:

35.20 m

Explanation:

By the law of conservation of energy we have,

mg(H-h)=\frac{1}{2}mv^2

g(H-h)=\frac{1}{2}v^2

\Rightarrow H=\frac{v^2}{2g}+h

where m= mass of the skier, h= 3.00 m

D= horizontal distance=13.9 m

H= maximum height attained

Also, the horizontal distance covered by the skier is

D=vt

=v\frac{2g}{h}

\Rightarrow v^2=\frac{gD^2}{2h}

thus, height H in terms of D  is given by

H=\frac{D^2}{2h}+h

H=\frac{13.9^2}{2\times3}+3

H=35.20 m

4 0
3 years ago
When hydrogen is burned in the presence of oxygen it will form water as per the equation: 2h2
Natasha_Volkova [10]

Answer:

B. In the first case, a combination reaction takes place and in the second case, a decomposition reaction takes place.

Explanation:

When hydrogen burns in oxygen, water is formed and when water is electrolysed then hydrogen and oxygen are produced. What type of a reaction takes place?

(i) In the first case,

(ii) In the second case?

A. In both the cases, i.e. (i) and (ii), a combination reaction takes place.

B. In the first case, a combination reaction takes place and in the second case, a decomposition reaction takes place.

C. In the first case, a combination reaction takes place and in the second case, a displacement reaction takes place.

D. In the first case, a displacement reaction takes place and in the second case, a decomposition reaction takes place.

Answer :

Hint: When hydrogen burns in air, H2H2 reacts with O2O2 to form water molecules. Here two reactants combine to form a single product. And, when water is electrolysed into hydrogen and oxygen, here a single compound decomposes into more than one product.

Complete step by step answer:

In the First case:

When hydrogen burns in oxygen, water is formed.

Hydrogen + Oxygen = Water

2H2+O2→2H2O2H2+O2→2H2O

When two reactants elements combine to form a single component, then this reaction is called the combination reaction. So, in this case, two reactants i.e. Hydrogen and oxygen combine to form a single product i.e. water molecules and heat is also released.

In the Second case:

When water is electrolysed then hydrogen and oxygen are produced.

2H2O→2H2+O22H2O→2H2+O2

When a single reactant is decomposed or broken down into two or more products, it is known as decomposition reaction. Here, a single reactant i.e. water, breaks or decomposes up to form two or more simple products i.e. hydrogen and oxygen. This decomposition reaction takes place by the action of electricity. So, we can see that in the first case, a combination reaction takes place and in the second case, a decomposition reaction takes place.

Therefore, the correct answer is option (B).

Note: Hydrogen is combustible and it burns with a popping sound in oxygen with an almost colourless flame to form water molecules and release heat. This reaction is highly exothermic. Hydrogen must be handled very carefully as the mixture of hydrogen and oxygen can be explosive when two are present in a particular ratio.

7 0
2 years ago
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bagirrra123 [75]

Answer:

The answer is "No, Hoverboards are risky, and riders are in danger of falling".

Explanation:

It's also known as a self-balanced scooter, it handheld electrical devices traveling on two wheels are hoverboards. It dominated the industry around 2015 and since then has become more and more successful. A rider is balanced on a frame between these wheels, driven by battery-powered lithium-ion batteries.

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