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
MrRissso [65]
3 years ago
8

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks along the x-axis from the spotlight toward the bui

lding at a speed of 1.4 m/s, which is taken as the given dx/dt, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? Step 1
Physics
1 answer:
Assoli18 [71]3 years ago
4 0

Answer:

\frac{dy}{dt}=-4.2m/s

Explanation:

Now, in order to solve this problem we must start by representing it with a drawing. (See attached picture). Notice in the drawing that we are dealing with similar triangles, so we need to build our equation based on the similar equations. So let's build our equation:

\frac{y}{2}=\frac{12}{12-x}

Now, we can solve the equation for y, so we get:

y=\frac{24}{12-x}

now we can differenciate this equation, we can start by turning the fraction into a negative power, like this:

y=24(12-x)^{-1}

Nex we can differenciate the function by using the power and the chain rules, so we get:

\frac{dy}{dt}=-24(12-x)^{-2}(-1)

or:

\frac{dy}{dt}=\frac{24}{(12-x)^{2}} \frac{dx}{dt}

so now we can substitute the values we know:

\frac{dy}{dt}=\frac{24}{(12-4)^{2}} (-1.4)

when solving we get:

\frac{dy}{dt}=-4.2m/s

so the shadow decreases at a rate of -4.2m/s.

You might be interested in
What a neurology professor does = _______ brains
Natasha_Volkova [10]
That’s really easy ask your teacher and also peace happy
3 0
2 years ago
find the mass of a ball on a roof 30 meters high, if the ball's gravitational potential energy is 58.8 joules
Sidana [21]
We are given the gravitational potential energy and the height of the ball and is asked in the problem to determine the mass of the ball. the formula to be followed is PE = mgh where g is the gravitational acceleration equal to 9.81 m/s^2. substituting, 58.8 J = m*9.8 m/s^2 * 30 m; m = 0.2 kg.
3 0
2 years ago
Read 2 more answers
Is there carbon atoms in the compound Ca3N2​
katen-ka-za [31]

No, there are not any carbon atoms inside this compound.

The compound is Ca_3N_2. This means there are 3 "Ca" atoms and 2 "N" atoms.

  • Ca is calcium
  • N is nitrogen

Thus, none of the elements in this compound are carbon, meaning there are no carbon atoms. Let me know if you need any clarifications, thanks!

~ Padoru

3 0
3 years ago
Read 2 more answers
Bill is farsighted and has a near point located 121 cm from his eyes. Anne is also farsighted, but her near point is 74.0 cm fro
Arada [10]

Answer:

Explanation:

The lens equation is

1 / f = 1 / di + 1 / do

Where

f is focal length

di is the image distance

do is the object distance

Both Annie and Billy use a glass whose near point is 25cm

Then, the object distance is

do = 25 - 2 = 23cm

The have the same object distance.

Let find the vocal length of bills eye

Given that,

Bill near point is 121cm and distance of the glass from the eye is 2cm

Then,

Image distance of bill is

di_B = -(121-2) = -119cm

object distance do = 23cm

Then,

1 / f_B = 1 / di_B + 1 / do

1 / f_B = -1 / 119 + 1 / 23

1 / f_B = -119^-1 + 23^-1

1 / f_B = 0.0351

Then, f_B = 28.51 cm

Also, let find Annie focal length

Given that,

Annie near point is 74 cm and distance of the glass from the eye is 2cm

Then,

Image distance of Annie is

di_A = -(74-2) = -72cm

object distance do = 23cm

Then,

1 / f_A = 1 / di_A + 1 / do

1 / f_A = -1 / 72 + 1 / 23

1 / f_A = -72^-1 + 23^-1

1 / f_A = 0.02959

Then, f_A = 33.8 cm

Distance of object from the lens when Annie uses Billy glass

Then,

1 / f_B = 1 / di_A + 1 / do

1 / 28.51 = -1 / 72 + 1 / do

28.51^-1 = -72^-1 + do^-1

do^-1 = 28.51^-1 + 72^-1

do^-1 = 0.048964

do = 20.42 cm

Then, the object location from the eye will be, the eye is 2cm from the glass. Then,

do_A = 20.42 + 2 = 22.42cm

do_A = 22.42 cm

Distance of object from the lens when Billy uses Annie glass

Then,

1 / f_A = 1 / di_B + 1 / do

1 / 33.8 = -1 / 119 + 1 / do

33.8^-1 = -119^-1 + do^-1

do^-1 = 33.8^-1 + 119^-1

do^-1 = 0.03799

do = 26.32 cm

Then, the object location from the eye will be, the eye is 2cm from the glass. Then,

do_B = 26.32 + 2 = 28.32 cm

do_B = 28.32 cm

7 0
3 years ago
Both the lens and the cornea of the eye have a primary function of
3241004551 [841]

Answer: B. bending light

Explanation:

The phenomenom of vision in human eye is thanks to refraction (when light changes its direction as it passes through one medium to another), and this is what the cornea and the lens do.

When the ray of light encounters the eye, the first thing it finds is the <u>cornea</u>, which<u> bends this ray and begins to form an image</u>, then light passes through the <u>pupil</u>, which is in charge of regulating the amount of light that enters in the eye.  

After light travels through pupil it passes through the <u>lens</u>, where <u>the rays of light change the direction again in order to focus the formed image on the retina. </u>

At this point it is important to note the formed image is downward, then the retina transforms light into electrical impulses that are sent to the brain through the optic nerve and finally the brain interprets these messages, and forms a right upward image.

In the image attached these parts can be seen.

6 0
3 years ago
Other questions:
  • As the temperature increases the number of effective collisions between reacting particles in a chemical reaction
    6·1 answer
  • As Earth moves around the Sun, its _____ is approximately perpendicular to the force of gravity exerted by the Sun.
    5·2 answers
  • Suppose a car is traveling at +25.0 m/s, and the driver sees a traffic light turn red. After 0.340 s has elapsed (the reaction t
    12·1 answer
  • How much work is required to compress a gas from a volume of 5.0 l to a volume of 2.5 l by exerting a constant external pressure
    9·1 answer
  • Michael Jordan, el célebre basquetbolista, ganó el torneo de clavadas de la NBA en 1988. Para lograr la hazaña saltó 1.35 metros
    15·1 answer
  • A dart is loaded into a spring-loaded toy dart gun by pushing the spring in by a distance d. For the next loading, the spring is
    6·1 answer
  • Juan, a biologist, notices that a particular group of hummingbirds leaves during the colder winter months and returns during the
    13·1 answer
  • Question 2 Multiple Choice Worth 2 points)
    14·1 answer
  • 9) Suppose it takes a plane 5 hours to travel from Philadelphia to San Francisco. It
    9·1 answer
  • Below are three graphs. The shape of graph 3 shows that the current flowing through this component is __________ proportional to
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!