A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.1 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building
Answer:
[tex]\frac{dh}{dt}=-0.4125 m/s[/tex]
Explanation:
The very first thing we can do here is to draw a sketch of the situation the problem is presenting. (See attached picture)
As you may see in the picture, we can suppose the spotlight is directly located on the ground so the light of the spotlight together with the person and the wall make two similar triangles.
In this case we need to think about the dimensions of the triangle that will change over time. We will call them:
x= distance between the spotlight and the man.
h= height of the shadow.
So we can build a relation between the height and the length of each triangle:
[tex]\frac{h}{12}=\frac{2}{x}[/tex]
the distance between the spotlight and the wall is constant, so I can directly write the 12 in my equation and the height of the man is constant as well, so I can write the 2 directly into the equation.
Next, we can solve the equation for h (since we are interested in figuring out how fast the height of the shadow is decreasing) so we get:
[tex]h=\frac{24}{x}[/tex]
So next, we need to take the derivative of the equation, since the derivative of a position function will give us the velocity at which that position is changing.
First we rewrite the equation like this:
[tex]h=24x^{-1}[/tex]
and take the derivative:
[tex]dh=-24x^{-2}dx[/tex]
we can rewrite the derivative like this:
[tex]\frac{dh}{dt}=-\frac{24}{x^{2}} \frac{dx}{dt}[/tex]
where:
dh/dt is the velocity at which the height of the shadow is decreasing (that's why our equation has a negative sign in front of it).
dx/dt is the velocity at which the value of x is increasing. In other words, how fast the man is moving away from the spotlight.
So we can go ahead and substitute:
we wish to find the velocity at which the shadow's height is decreasing when the distance between the man and the building is 4m, so in this case, x=12-4=8m
[tex]\frac{dh}{dt}=-\frac{24}{8^{2}}(1.1 m/s)[/tex]
so we get:
[tex]\frac{dh}{dt}=-0.4125 m/s[/tex]
What are the units for measuring specific heat?
a. degrees Celsius per gram
b. joules per degrees Celsius
c. joules per gram degree Celsius
d. degrees Celsius per joule gram
Answer:
c. joules per gram degree Celsius
Explanation:
edg 2021
If at some point in time an object has zero velocity and zero acceleration, what does that mean about its motion at the next instant
Answer:
Explanation:
Usually, when an object possesses 0 velocity, then the object is expected to be at rest. But like the popular saying, there's always an exception to every rule. There exists cases in which an object isn't at rest, but possesses 0 speed or velocity. Since acceleration is the rate of change of velocity with time, the acceleration becomes negative, instead of positive.
Again, when the acceleration becomes zero, it means that the object isn't moving or it has no speed. And thus, the body is at rest. Every moving body as an acceleration, either positive, or negative. Zero acceleration means the object is at rest, and not moving at all.
Please leave a like if it helped you
At any point in time, when
when the acceleration becomes zero, it means that the object isn't moving or it has no speed. And thus, the body is at rest.
What is acceleration?Acceleration is defined as the change of the velocity with the time. Acceleration is a vector quantity and is defined by both the magnitude and the direction
when the acceleration becomes zero, it means that the object isn't moving or it has no speed. And thus, the body is at rest. Every moving body as an acceleration, either positive, or negative. Zero acceleration means the object is at rest, and not moving at all.
Now If an object is moving with an acceleration that causes its speed to be reduced, there will be a moment in which it reaches v = 0, but this doesn't necessarily mean that the acceleration isn't acting anymore. If the object continues its movement with the same acceleration, it's velocity will become negative.
If you throw an object in the air with a certain velocity, it will move vertically, reducing its velocity in a 9,8 rate (which is the acceleration caused by gravity). At a certain point, the object will reach its maximum height, and will start to fall. In the exact moment that it reaches the maximum height, before it starts falling, its velocity is zero, but gravity is still acting on the object (this is the reason why it starts falling instead of just being stopped at that point). Therefore, at that point, the object has zero velocity but an acceleration of 9,8 .
To know more about acceleration follow
brainly.com/question/25749514
explain why ionizing radiation is dangerous?
Answer:
When the dose is high enough, ionizing radiation causes two types of harm to humans: direct tissue damage and cancer. Direct tissue damage happens when enough molecules are broken apart that the cells simply can no longer function. This can lead to radiation burns, radiation sickness, organ failure, and even death.
Ben runs from a position 3 m west of Main Street to a new position 45 m
west of Main Street in 6 seconds. What is Ben's velocity?
O
A. 7 m/s east
B. 7 m/s west
C. 8 m/s west
O
O
D. 8 m/s east
SUBMIT
Answer:
Option B. 7 m/s West.
Explanation:
From the question given above, the following data were obtained:
Position 1 (P₁) = 3 m West
Position 2 (P₂) = 45 m West
Time (t) = 6 s
Velocity (v) =?
Next, we shall determine the displacement of Ben. This can be obtained as follow:
Position 1 (P₁) = 3 m West
Position 2 (P₂) = 45 m West
Displacement =?
Displacement = P₂ – P₁
Displacement = 45 – 3
Displacement = 42 m West
Finally, we shall determine the velocity of Ben. This can be obtained as follow:
Time (t) = 6 s
Displacement (d) = 42 m West
Velocity (v) =?
v = d/t
v = 42 m West / 6 s
v = 7 m/s West
Thus the velocity of Ben is 7 m/s West
An air-filled capacitor stores a potential energy of 6.00 mJ due to its charge. It is accidentally filled with water in such a way as not to discharge its plates. How much energy does it continue to store after it is filled
This question is incomplete, the complete question is;
An air-filled capacitor stores a potential energy of 6.00 mJ due to its charge. It is accidentally filled with water in such a way as not to discharge its plates. How much energy does it continue to store after it is filled?
(The dielectric constant for water is 78 and for air it is 1.0006.)
Answer: it continue to store 0.07692 mJ after it was filled
Explanation:
Given that;
stored potential energy = 6.00 mJ = 0.006 J
dielectric constant for water K = 78
Energy stored U = Q² / 2C = 0.006 J
C = ∈₀A/d { Air}
C = K∈₀A/d { Water, k = 78 }
so
U = 0.006 / 78
U = 7.6723 × 10⁻⁵J
U = 0.07692 mJ
Therefore it continue to store 0.07692 mJ after it was filled
PLz help I will give you brainliest for real
How you feel on days when you do exercise compared to days when you don't exercise
Answer:
When i do exercise i feel great and happy afterwards ( there is a proven fact that after you go on a run, play a sport, or exercise you are proven to be more upbeat )
When i don't exercise i feel kinda lazy and tired mostly bored.
A 1248 kg car is pulled by a tow truck that has an acceleration of 2.0 m/s2. What is the
net force on the car?
Answer: = 2,496 N
Explanation:
Force is the push or pull on an object and it is calculated as:
= Mass * Acceleration
= 1,248 * 2.0
= 2,496 N
What is the potential energy of a 2500 g object suspended 5 kg above the earth's surface?
kilograms.
Answer:
[tex]potential \: energy = mgh \\ = ( \frac{2500}{1000} ) \times 10 \times 5 \\ = 125 \: newtons[/tex]
if height is 5 m
What is the purpose of the Bill of Rights?
to inspire the governments of other nations
to limit the rights of individual citizens
to explain the procedure for amending the Constitution
to guarantee freedoms that belong to every citizen
Answer:
i think it is To limit the rights of individual citizens
Explanation:
A woman holds a frozen smoothie in her hand on a warm
day.
Which photo shows the direction of thermal energy transfer?
O A.↕️
B
C ⬆️
D⬇️
Answer:
C
Explanation:
The thermal energy from her hand will go up into the smoothie.
Answer:
C bois
Explanation:
A person holds onto an object for 2 minutes but doesn't move the object. Is work done
on the object?
Answer:
No
Explanation:
What is the standard form for 2 × 10−3 ?
Answer:
17
Explanation:
2 x 10 = 20
20-3 = 17
Two hockey pucks with mass 0.1 kg slide across the ice and collide. Before
the collision, puck 1 is going 15 m/s to the east and puck 2 is going 12 m/s to
the west. After the collision, puck 2 is going 15 m/s to the east. What is the
velocity of puck 1?
Answer:
Puck 1 = 12 m/s
Explanation:
Conservation of energy
KE_1a + KE_2a = KE_1b + KE_2b
(1/2)(0.1kg)(15m/s)^2 + (1/2)(0.1kg)(12m/s)^2 = (1/2)(0.1kg)(V)^2 + (1/2)(0.1kg)(15m/s)^2
V = 12m/s
Answer:
12 m/s west
Explanation:
just did it
why does the force of air resistance affect the motion of a person traveling at high speed more than a person walking across the room?
Answer:
yes .
Explanation:
...
;-; :) have a good day
Answer:
because on air the speed is high compared to walking
Please answer the questions... I will surely mark you as the brainliest according to me :)
Answer:
(a) You can tell that have the same strength because they have attracted the same amount of paper clips.
(b) Iron is used in electromagnets because steel retained magnetic properties after the power was turned off, but in the iron, the paper clips dropped off right away.
An object has a mass of 20 kg and is placed 2 m above the ground. What is its gravitational potential energy? (PEg)
Answer:
392 JExplanation:
The potential energy of a body can be found by using the formula
PE = mgh
where
m is the mass
h is the height
g is the acceleration due to gravity which is 9.8 m/s²
From the question we have
PE = 20 × 9.8 × 2
We have the final answer as
392 JHope this helps you
Last week Tasha and Amy got into a fight at school. Tasha is accusing Amy of talking behind her back. Since the fight, Tasha has been
spamming Amy's social media profile with posts calling her a backstabber, a liar, and a cheat, among other things, Amy insists the matter was
all a misunderstanding, but some of her friends have started to turn against her.
In this situation Amy should try to confront Tasha face to face to sort the matter out. (5 points)
O True
O False
Answer:
True
Explanation:
Answer:
True
Explanation:
I feel that if she tries sorting it out herself that it could go two ways.
A slide projector projects images on a screen. a) If the slide is 15.5 cm from the lens and the lens has a focal length of 15 cm, how far away is the screen
Answer:
[tex]d_{i}=465 cm=4.65 m[/tex]
Explanation:
Using the thin lens equation, we have:
[tex]\frac{1}{f}=\frac{1}{d_{o}}+\frac{1}{d_{i}}[/tex]
Where:
f is the focal length
d(o) is the distance of the object
d(i) is the distance of the image
[tex]\frac{1}{15}=\frac{1}{15.5}+\frac{1}{d_{i}}[/tex]
[tex]\frac{1}{15}-\frac{1}{15.5}=\frac{1}{d_{i}}[/tex]
[tex]d_{i}=465 cm=4.65 m[/tex]
Therefore, the screen is at 465 cm.
I hope it helps you!
the motion diagrams shown above represent cyclist 1 in the third panel above?
Answer:
A
Explanation:
Change of velocity is defined as acceleration and acceleration accounts for both change is direction and speed
Suppose that when spring was wound, 100J of work was done but 15J escaped to the surrounding as heat. The change in internal energy of the spring is?
Answer: 85J
Explanation:
From the question, we are informed that when spring was wound, 100J of work was done but 15J escaped to the surrounding as heat.
Therefore, the change in internal energy of the spring will be calculated as:
ΔU = q + w
where, q = -15J
w = 100J
ΔU = -15J + 100J
= 85J
how much does a dog of 10kg mass weigh in newtons?
Answer:
98.0665 newtons
have a good day :]
A 0.53 kg arrow leaves a bowstring at a velocity of 63 m/s. If the arrow was initially at rest and then the string applied a force on it for 7 x 10-3 seconds, what was the approximate average force in Newtons that acted on the arrow during this time?
Answer:
4770 N
Explanation:
Momentum is the product of mass and velocity and force is the change in momentum divided by change in time.
Given from the question;
Mass of arrow= 0.53 kg
Velocity of arrow = 63 m/s
Initial velocity of arrow = 0 m/s
Change in time = 0.007 s
Finding momentum after the arrow is released as;
p=m*v
p= 0.53 * 63
p= 33.39 kg*m/s
Force is the change in momentum divided by change in time;
F= 33.39 / 0.007
F= 4770 N
9 The friction between the car and the mud is equivalent to the__________________.
(a) Resultant force
(b) Drag force
(c) Equivalent force
(d) Stretch force
(e) None
I need help with this please
Answer:
1. The respiratory system functions when our involuntary nervous system sends impulses to the muscles in the diaphragm; thereby, causing the lungs to expand and contract.
2. The respiratory system oxygenates the blood which is vital for bodily function as oxygenated blood is carried from your lungs to the left side of your heart, to be circulated throughout the body. Furthermore deoxygenated blood is carried back to the right side of your heart to get oxygenated once more.
3. The other body systems that are crucial for the lungs to function are the nervous system and the muscular system.
4. without the raspatory system the body wouldn't receive any oxygen and the brain would slowly die. therefore, without the brain the heart would stop functioning and atrophy etc.
Explanation:
Select all the correct answers.
Bella is writing a research paper on ocean currents. Which two sources should she consult?
an article published by a university or a government agency
an article from a website containing advertisements
an article published in 2015 and updated a week ago
an article appearing in the blog post of a teenage surfer
an article that does not state the author’s name and details
Answer: I belive the answer is
an article published by a university or a government agency and an article published in 2015 and updated a week ago
a suspension bridge cable is connected to its anchor at a 20 degree angle. calculate the vertical component force on the anchor by the cable.
The question is missing some parts. Here is the complete question.
A suspension bridge cable is connected to its anchor at a 20° angle. Find the vertical and horizontal component of the force on the anchor by the cable.
Answer: [tex]F_{x}=[/tex] 14095.4 N
[tex]F_{y}=[/tex] 5130.3 N
Explanation: The force applied to the anchor is not perpendicular to the horizontal plane. So, it can be decomposed into 2 components: a vertical component, which is on the y-axis, and a horizontal component, which is on the x-axis.
The force and its components forms a right triangle, so we can calculate the components by using trigonometric relations:
Horizontal
[tex]cos(20)=\frac{F_{x}}{F}[/tex]
[tex]F_{x}=F.cos(20)[/tex]
[tex]F_{x}=15,000(0.9397)[/tex]
[tex]F_{x}=[/tex] 14,095.4 N
Vertical
[tex]sin(20)=\frac{F_{y}}{F}[/tex]
[tex]F_{y}=Fsin(20)[/tex]
[tex]F_{y}=[/tex] 15,000(0.3420)
[tex]F_{y}=[/tex] 5,130.3 N
The vertical and horizontal components of force on the anchor by the cable are 5130.3 N and 14095.4 N, respectively.
How does the First Amendment affect religion in the United States?
A specific religion can not be manditory
There can be no religion in the United States
State employees cannot have a religion
The government has an official religion
Answer:
A
Explanation:
An object of mass 30 kg is falling in air and experiences a force due to air resistance of 50 newtons. Calcuate the acceleration of the object
Answer:
this answer you question
If the angle between two forces increases, the magnitude of their resultant-
A Decreases
C. Remain unchanged
D. Decrease than decreases