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
How long was a 60 W light bulb turned on if it used a total of 580 J of energy?
icang [17]
Here's the tool you need.  You can't answer the question without this:

           "1 watt"
means
           "1 joule of energy, generated, used, or moved, every second".

So      60 watts  =  60 joules per second

           Total energy generated,
            used, or moved                  = (power) x (time).

                                     580 joules  =  (60 watts) x (time)

Divide each side
by  (60 watts):              Time  =  (580 joules) / (60 joules/sec) 

                                               =  (9 and 2/3)  seconds  .
7 0
3 years ago
Please help on this one?
Lynna [10]
Object distances are always negative according to the Cartesian sign convention
3 0
3 years ago
Which of the following BEST represent a good plan for decreasing your BMI?
Deffense [45]
I’d say b is the better option because d is starving yourself which creates unhealthy habits, c would cause yo yo dieting or binging because you treat food as a reward which is a toxic mindset, and a same explanation. I wish there was an answer to just track what you eat, have daily exercise and enjoy in moderation, though.
3 0
3 years ago
AYUDAAA! <br> Hola, alguien podría ayudarme en esto la C), me ha complicado demasiado!!
Softa [21]

Answer:

I dont know spanish... and i live in Cali... wow....

Explanation:

6 0
2 years ago
A soccer player carries the ball for a distance of 40.0 m in the direction 42.0° west of south. find the westward component of t
Maksim231197 [3]

Actually what the problem meant about the westward component of the ball’s displacement is the horizontal component of the displacement. To help us better understand the problem, I attached a figure of the situation.

We can see from the figure that to solve for the value of the horizontal component, we have to make use of the sin function. That is:

sin θ = side opposite to the angle / hypotenuse of the triangle

sin 42 = x / 40 m

x = (40 m) sin 42

x = 26.77 m

 

Therefore the ball has a westward displacement of about 26.77 m

3 0
3 years ago
Other questions:
  • When a cup is placed on a table, which force prevents the cup from falling to the ground?
    8·1 answer
  • How long does it take electrons to get from the car battery to the starting motor? Assume the current is 143 A and the electrons
    13·1 answer
  • How does kinetic energy affect the stopping distance of a vehicle traveling at 30 mph compared to the same vehicle traveling at
    10·1 answer
  • If 3.5 paper clips = 1.0 pencils and your paper is 1.5 pencils long, how many paper clips long is your paper?
    12·1 answer
  • The primary difference between a barometer and a manometer is
    11·1 answer
  • Does charged battery have energy
    6·2 answers
  • PLS ANSWER FAST WILL GIVE BRAINLEST!!!!
    7·1 answer
  • Pls someone help 10points!!!
    9·1 answer
  • If a pitcher throws a baseball 10 m in 30 seconds - what would be the average speed of the baseball
    12·1 answer
  • What causes satellites to remain in orbit above Earth?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!