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
Olenka [21]
2 years ago
7

tourist travels 1500 miles using two planes. The second plane averages 50 miles per hour faster than the first plane. The touris

t uses the slower plane for the first 500 and the faster plane for the next 1000 miles. The total flying time is 6.5 hours. What is the speed of the first plane?
Physics
1 answer:
melamori03 [73]2 years ago
5 0

Answer:

V₁ = 200 mi/h

Explanation:

To do this, we need to analyze the given data.

We have a total distance and time of 1500 mi and 6.5 h. We also know that the second plane goes 50 mi/h faster than the first plane, (V₂ = V₁ + 50). The firsts 500 miles were on the first plane and the remaining 1000 mi with the second plane.

Using the expression of distance, and assuming a constant speed in both planes we have:

d = V * t   (1)

Replacing this expression for both planes we have:

d₁ = V₁ * t₁

d₂ = (V₁+50) * t₂

WE are missing several data, because we do not know the times for each plane, but we can have a clue.

The total time of flight was 6.5 h, this is equivalent to just sum both times of both planes, so:

t = t₁ + t₂   (3)

From the expressions of distance for both planes, we can solve for time, and then replace in the above expression of the total time. In that way we can solve for the speed of the plane. Let's solve for both times in the planes:

t₁ = d₁ / V₁ = 500/V₁    (4)

t₂ = d₂ / V₁+50 = 1000/ V₁ + 50   (5)

Now, all we have to do is replace (4) and (5) into (3) and solve for V₁:

6.5 = [(500/V₁) + (1000/V₁ + 50)

6.5 = [500*(V₁+50) + 1000V₁ / V₁(V₁+50)]

6.5 = [500V₁ + 25000 + 1000V₁ / V₁² + 50V₁

6.5(V₁² + 50V₁) = 1500V₁ + 25000

6.5V₁² + 325V₁ - 1500V₁ - 25000 = 0

6.5V₁² - 1175V₁ - 25000 = 0

From here, we use the quadratic equation to solve for V₁:

X = 1175 ± √(1175)² + 4 * 6.5 * 25000 / 2 * 6.5

X = 1175 ± √1380625 + 650000 / 13

X = 1175 ± 1425 / 13

X₁ = 1175 + 1425 / 13 = 200

X₂ = 1175 - 1425 / 13 = -19.23

So, it's very clear that the speed cannot be negative, so we stick with the first value. Therefore the speed pf the first plane is:

<h2>V₁ = 200 mi/h</h2><h2>V₂ = 250 mi/h</h2>

Hope this helps

You might be interested in
Communications satellites are placed in orbits so that they always remain above the same point of the earth's surface.A Part com
masya89 [10]

Answer:

24 hours

7\times 10^{-5}\ rad/s

Explanation:

If a satellite is in sync with Earth then the period of each satellite is 24 hours.

T=24\times 60\times 60\ s

Angular velocity is given by

\omega=\dfrac{2\pi}{T}\\\Rightarrow \omega=\dfrac{2\pi}{24\times 60\times 60}\\\Rightarrow \omega=7\times 10^{-5}\ rad/s

The angular velocity of the satellite is 7\times 10^{-5}\ rad/s

3 0
3 years ago
Given a 10-V power supply, would a 20-ohm resistor and a 5-ohm resistor need to be arranged in parallel or in series to generate
Bogdan [553]

Answer:

The resistors will be in parallel to produce a net resistance of 4ohm and current in 20 ohm resistor will be 0.5A and 5ohm resistor will be 2A.

Explanation:

We are given 10 voltage power source and we have two Resistors with resistance of 20 ohm and 5ohm.

We need to find the orientation in which these two resistors would be arranged so that the circuit could get a current of 2.5Ampere.

Using ohm's law we have

V = I*R

V= voltage

I= current

R= resistance

10 = 2.5*R

R = 10/2.5 = 4ohm

that means we need a total of 4ohm resistance from these two resistors.

since the net Resistance(4ohm) is lower than the smallest resistance(5ohm) available that means the orientation of the resistors will be in parallel.

\frac{1}{R} = \frac{1}{R1} +\frac{1}{R2}\\                 = \frac{1}{20} +\frac{1}{5}\\ \\                 = \frac{1+4}{20} =\frac{1}{4}

R(net) =4ohm

Now the orientation of the resistors are in parallel so the current will be divided.

we know that the current will divide in opposite manner the arm which provides more resistance less current will flow from there and vice versa.

We know that the voltage in parallel remains same

In 20 ohm resistance

again using ohms law

V = i1*R1

10 = i1*20

i1 = 0.5A

in 5ohm resistor

V=i2*R2

10 = I2*5

i2 =2A

and i1+i2 = 0.5+2= 2.5A which means our calculation is correct.

Therefore the resistors will be in parallel to produce a net resistance of 4ohm and current in 20 ohm resistor will be 0.5A and 5ohm resistor will be 2A.

6 0
2 years ago
Two containers (A and B) are in thermal contact with an environment at temperature T = 280 K. The two containers are connected b
zmey [24]

Answer:

The maximum amount of work is  W = 1563.289 \ J

Explanation:

From  the question we are told that

   The temperature of the environment is  T = 280\ K

    The volume of container A is  V_A = 2 m^3

    Initially the number of moles  is  n = 1.2 \ moles

     The volume of container B is V_B = 3.5 \ m^3

     

At equilibrium of the gas the maximum work that can be done on the turbine is mathematically represented as

             W =  P_A V_A  ln[ \frac{V_B}{V_A} ]

Now from the Ideal gas law

          P_A V_A =  nRT

So substituting for P_A V_A in the equation above

          W =  nRT ln [\frac{V_B}{V_A} ]

Where R is the gas constant with a values of  R =  8.314 \  J/mol

Substituting values we have that

            W = 1.2 * (8.314) * (280) * ln [\frac{3.5}{2} ]

          W = 1563.289 \ J

8 0
3 years ago
What happens to air pressure as altitude decreases
Ksivusya [100]
Pressure decreases with increasing altitude. The pressure at any level in the atmosphere may be interpreted as the total weight of the air above a unit area at any elevation. At higher elevations, there are fewer air molecules above a given surface than a similar surface at lower levels.
8 0
3 years ago
Read 2 more answers
What part of the gun position equipment supports all of the elevating parts of the gun?
BARSIC [14]
The gunstock it’s also called stock or shoulder stock
5 0
3 years ago
Other questions:
  • Bill and Mary wanted to have a snack after school. They heated some milk in a pot on the stove to make hot chocolate. They also
    10·1 answer
  • If a light bulb is missing or broken in a parallel circuit will the other bulb light?
    7·1 answer
  • Water waves in a shallow dish are 7.0 cm long. At one point, the water moves up and down at a rate of 4.0 oscillations per secon
    13·1 answer
  • In which type of process is a gas heated so rapidly that is expands before any heat can escape, resulting in an absence of heat
    9·1 answer
  • . 1 A voltmeter has high resistance. Explain why?​
    14·2 answers
  • Who is the winner of khatron khiladi made in india 2020​
    13·2 answers
  • You are holding a 1 kg rock and standing at the top of a cliff. You drop the rock off the cliff and it falls a distance 10 m. In
    9·1 answer
  • Materials A, B, and C are solids that are at their melting temperatures. Material A requires 200 J to melt 4 kg, material B requ
    13·1 answer
  • Why did humans first develop culture?
    14·1 answer
  • The International Space Station has a mass of 419,455 kg. When the station
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!