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
Olegator [25]
3 years ago
12

Two buses are driving along parallel freeways that are 5mi apart, one heading east and the other heading west. Assuming that eac

h bus drives a constant 55 mph, find the rate at which the distance between the buses is changing when they are 13mi apart, heading toward each other.

Physics
1 answer:
Oksanka [162]3 years ago
4 0

Answer:

101.54m/h

Explanation:

Given that the buses are 5mi apart, and that they are both driving at the same speed of 55m/h, rate of change of distance can be determined using differentiation as;

Let l be the be the distance further away at which they will meet from the current points;

l=\sqrt{13^2-5^2}=12m\\\\\frac{dl}{dt}=-(55m/h+55m/h})\\\\=-110m/h#The speed toward each other.

\frac{dh}{dt}=0, \ \ \ \ h=constant\\\\h^2+l^2=b^2\\\\2h\frac{dh}{dt}+2l\frac{dl}{dt}=2b\frac{db}{dt}\\\\2\times5\times0+2\times12\times(-110)=2\times13\frac{db}{dt}\\\\\frac{db}{dt}=-101.54m/h

Hence, the rate at which the distance between the buses is changing when they are 13mi apart is 101.54m/h

You might be interested in
A thermometer initially reading 212F is placed in a room where the temperature is 70F. After 2 minutes the thermometer reads 125
frez [133]

Answer:

91.3°F

Explanation:

Let T be the temperature of the thermometer at any time

T∞ be the temperature of the room = 70°F

T₀ be the initial temperature of the thermometer = 212°F

And m, c, h are all constants from the cooling law relation

From Newton's law of cooling

Rate of Heat loss by the cake = Rate of Heat gain by the environment

- mc (d/dt)(T - T∞) = h (T - T∞)

(d/dt) (T - T∞) = dT/dt (Because T∞ is a constant)

dT/dt = (-h/mc) (T - T∞)

Let (h/mc) be k

dT/(T - T∞) = -kdt

Integrating the left hand side from T₀ to T and the right hand side from 0 to t

In [(T - T∞)/(T₀ - T∞)] = -kt

(T - T∞)/(T₀ - T∞) = e⁻ᵏᵗ

(T - T∞) = (T₀ - T∞)e⁻ᵏᵗ

Inserting the known variables

(T - 70) = (212 - 70)e⁻ᵏᵗ

(T - 70) = 142 e⁻ᵏᵗ

At t = 2 minute, T = 125°F

125 - 70 = 142 e⁻ᵏᵗ

55/142 = e⁻ᵏᵗ

- kt = In (55/142) = In (0.3873)

- k(2) = - 0.9485

k = 0.4742 /min

At time t = 4 mins

kt = 0.4742 × 4 = 1.897

(T - 70) = 142 e⁻ᵏᵗ

e^(-1.897) = 0.15

T - 70 = 142 × 0.15 = 21.3

T = 91.3°F

7 0
3 years ago
What happens to the radiation coming from the Sun and heading towards Earth?
miss Akunina [59]

Answer: some of the energy are shielded away by the ozone layer,

The rest warm the earth

Explanation:

Not all energy from the sun reaches the earth, some of the energy are shielded away by the ozone layer while the rest energy warm the earth

7 0
3 years ago
Which statement accurately describes the ultraviolet catastrophe
castortr0y [4]

Answer: A hot lightbulb gave off white visible light instead of ultraviolet light.

Explanation:

3 0
3 years ago
When the rocket launched the astronauts aboard experienced an acceleration of 32 m/s^2. If one of the astronauts had a mass of 6
sergij07 [2.7K]

Answer:

The question is somewhat vague in that acceleration is not exactly defined:

Usually a = (v2 - v1) / t    which would imply that

a = 32 / g = 32 / 9.8 = 3.27   the acceleration due to change in speed of the rocket

One can also say that the astronaut experiences an acceleration of 9.8 m/s^2 just by being motionless on the surface of the earth.

Then a = (32 - 9.8) / 9.8 = 2.27 due to the acceleration of the rocket

If we assume the first condition then

F = 65 kg * 3.27 * 9.8 m/s^2 = 2083 N

7 0
2 years ago
Technician A says that the accumulator is on the high-pressure side of the refrigerant system. Technician B says that the receiv
pychu [463]

Question:

The options are

a. Technician A only

b. Technician B only

c. Both A and B

d. Neither A nor B

Answer:

The correct option is

d. Neither A nor B

Explanation:

Here, we note that to locate the receiver/driers we look at the high-pressure side of refrigerant system normally around the tubes in between the expansion valve outlet and the condenser outlet and connected to the condenser.

While the accumulator can be found, attached to the evaporator outlet within the low pressure side of the refrigerant system.

Therefore, neither Technician A nor B is correct.

6 0
3 years ago
Other questions:
  • Define mechanical energy useing the example of the skateboarder on the half-pipe explain how kinetic and potential energy relate
    11·1 answer
  • In which of the following situation is light most likely to be a reflection
    9·1 answer
  • Suppose that you are holding a pencil balanced on its point. If you release the pencil and it begins to fall, what will be the a
    6·1 answer
  • At what temperature do the fahrenheit and celsius scales give the same reading?
    6·1 answer
  • A small 12.00 g plastic ball is suspended by a string in a uniform, horizontal electric field. If the ball is in equilibrium whe
    7·1 answer
  • Can someone tell me the answer for both of these pleaseeee i need it asap!!! i will give brainlist!!
    15·1 answer
  • Which of the following is one of the three main fuels that a star uses for fusion
    15·2 answers
  • What is your wheel and axle
    7·2 answers
  • A bicycle has a momentum of 23.4
    6·1 answer
  • A vertical, solid steel post 25 cm in diameter and 2.50m long is required to support a load of 8000kg. You can ignore the weight
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!