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
saw5 [17]
3 years ago
10

A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her orig

inal course, and flies 2 h in the new direction. If she maintains a constant speed of 675 mi/h, how far is she from her starting position?

Physics
1 answer:
atroni [7]3 years ago
4 0

Answer:

The plane is 2353.7 mi from the starting position.

Explanation:

Please, see the attached figure for a graphic representation of the problem.

We have 2 displacement vectors "a" and "b" and a vector "c" that is the sum of vectors "a" plus "b" (c = a + b). The module of "c" will be the distance of the plane from the starting point.

vector a = (xa, ya)

vector b = (xb, yb)

where “xa” and “xb” are the horizontal components of the vectors “a” and “b” respectively and “ya” and “yb” are the vertical components of each vector.

Then, the vector c = a + b will be:

c = (xa + xb, ya + yb)

The module of a vector is calculated using the following expression for a vector “v”:

module of v = \sqrt{x^{2} + y^{2} }

Then, the module of c will be:

module of c = \sqrt{(xa + xb)^{2} + (ya + yb)^{2}} = distance from starting point

Then, we have to find the components of vectors “a” and “b”

The distance traveled during the first 1.5 hours of the trip is the module of the vector “a”. Then:

module of a = \sqrt{xa^{2} + ya^{2} } = distance traveled during the first 1.5 hours.

The distance can be calculated using the equation of the position of an object moving in a straight line at constant speed:

x = x0 + v * t

where

x = position at time t

x0 = initial position

v = speed

t = time

Considering x0 as the starting point (x0 = 0)

x = 675 mi/h * 1.5 h = 1012.5 mi

Then:

module of a = \sqrt{xa^{2} + ya^{2} } = 1012. 5 mi

Since the plane moves only on the horizontal (see figure), the "y" component of the vector, "ya", will be 0.

Then:

(1012.5 mi)² = xa²

xa = 1012. 5mi

a = (1012.5 mi, 0)

In the same way, we have fo find the components of the vector “b”. The module of “b” will be the distance traveled during this part of the flight:

module of b = \sqrt{xb^{2} + yb^{2} } = x = x0 + v * t

Considering x0 as the point at which the plane turns (x0 = 0)

x = 675 mi / h * 2 h = 1350 mi

Using trigonometry, we can calculate xb and yb (see figure):

sin angle = opposite / hypotenuse

cos angle = adjacent / hypotenuse

In this case:

opposite = yb

adjacent = xb

hypotenuse = module of “b”

Then:

sin 10° = yb / module of “b”

sin 10° * module of “b” = yb

In the same way:

cos 10° * module of “b” = xb

Since module of “b” = 1350 mi

xb = 1329.5 mi

yb = 234.4 mi

b = (1329.5 mi, 234.4 mi)

The vector c = a+b can now be calculated:

c = (xa + xb, ya + yb)

c =(1012.5 mi + 1329.5 mi, 0 mi + 234.4 mi) = (2342 mi, 234.4 mi)

The module of c will be:

module of c = \sqrt{(2342 mi)^{2} + (234.4 mi)^{2} } = 2353.7 mi

The plane is 2353.7 mi from the starting position.

You might be interested in
Electric energy can be transferred into other types of energy we often experiences transformation of energy in our every day liv
Damm [24]

An amplifier.

Electrical energy provided to an amplifier is converted into sound energy as it is "fed" or provided to the speaker portion of an amplifier.

7 0
2 years ago
When the leaves are __________________, they fall straight down.
konstantin123 [22]

Answer:Done doing there job, in the winter they have a break

Explanation:

7 0
2 years ago
In a milkans apparatus,an oil drop of weight 2.0×10^-15kg accquires two surplus electrons. when a Potential difference of 620 vo
andriy [413]

Answer:

r = 9.92 mm

Explanation:

Given that,

Mass of oil drop, m=2\times 10^{-15}\ kg

It acquires 2 surplus electrons, q = +2e =3.2\times 10^{-19}\ C

Potential difference, V = 620 V

Thie potential difference is applied between the pair of horizontal metal plates the drop is in equilibrium.

We need to find the distance between the plates.

At equilibrium,

mg = qE

Since, E = V/r (r is distance between plates)

mg=\dfrac{qV}{r}\\\\r=\dfrac{qV}{mg}\\\\r=\dfrac{3.2\times 10^{-19}\times 620}{2\times 10^{-15}\times 10}\\\\=0.00992\ m\\\\=9.92\ mm

So, the distance between the plates is 9.92 mm.

6 0
2 years ago
A hand moves a block vertically upward. Its speed slows down as it moves up (it is decelerating). The work done by gravity on th
Nataly_w [17]

Answer:

a. negative

b. zero

Explanation:

work is the change in the energy of a system due to external forces

work is done when a force moves a load through a distance in the direction of the force

The work done by a force on a  system is positive when the force  and the force displacement point  in the same direction and negative  when they point in opposite  directions

in the scenario we are considering in the question, the force (the hand) moves the block vertically upwards but the displacement of the block reduces (in the opposite direction) since it decelerates. as such the work done by gravity on the block is negative.

the work done on the block is zero if the system consists of the block and the earth because there is no gravitational force exerted on the system

5 0
3 years ago
a transformer changes 95 v acorss the primary to 875 V acorss the secondary. If the primmary coil has 450 turns how many turns d
natita [175]

Answer:

The number of turns in the secondary coil is 4145 turns

Explanation:

Given;

the induced emf on the primary coil, E_p = 95 V

the induced emf on the secondary coil, E_s = 875 V

the number of turns in the primary coil, N_p = 450 turns

the number of turns in the secondary coil, N_s = ?

The number of turns in the secondary coil is calculated as;

\frac{N_p}{N_s} = \frac{E_p}{E_s}

N_s = \frac{N_pE_s}{E_p} \\\\N_s = \frac{450*875}{95} \\\\N_s = 4145 \ turns

Therefore, the number of turns in the secondary coil is 4145 turns.

8 0
3 years ago
Other questions:
  • How does an object move when it is subject to a steady centripetal force
    10·1 answer
  • PLZ HELP FAST!!!!!!!!!Which characteristics describe a maritime polar air mass? A.cold and humid air B.cold and dry air C.warm a
    8·1 answer
  • 70 POINTS!! Give a real life example showing how sensory neurons work with the motor neurons
    13·1 answer
  • A boy of 50 kg jumps off a boat (30 kg), causing the boat to move to the right at 2.0 m/s. In what direction and at what velocit
    8·2 answers
  • A 730-N man stands in the middle of a frozen pond of radius 5.0 m. He is unable to get to the other side because of a lack of fr
    11·1 answer
  • Which element could be described by the list of properties above?
    12·2 answers
  • Balanced or Unbalanced?
    13·1 answer
  • It decomposes in a first-order reaction with a rate constant of 14 s–1. how long would it take for an initial concentration of 0
    5·1 answer
  • 3 A picture is supported by two vertical strings; if the weighi
    9·1 answer
  • A body having mass 200g id moving with velocity 120m\s. What is its power​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!