Answer:
1) a = 17.3 m/s²
2) Fnet = 37.5 N
3) T = 16.2 N
Explanation:
1)
When the bucket is at the top of the circle, there are two forces acting on it: the tension force (T) which pulls from the bucket, so it is directed downward, and the force due to gravity, that also points downward, so both forces add:[tex]F_{net} = T + m*g (1)[/tex]According to Newton's 2nd Law, this net force must be equal to the mass of the bucket, times the acceleration.Now, due to the bucket is moving around a circle, there must be a force that keeps the bucket following a circular trajectory, that is the centripetal force, and always aims toward the center of the circle.This force is not a new type of force, it's always the net force that aims toward the center.At the top of the circle, because as the tension force as gravity point downward, the centripetal force, is just this net force.It can be showed that the centripetal force can be written as follows:[tex]F_{c} = m*a_{c} = m*\frac{v^{2}}{r} (2)[/tex]
Since we have already said that a = ac (At the top of the circle), we can solve (1) for a, simplifying and replacing v and r by their values, as follows:[tex]a = a_{c} = \frac{v^{2} }{r} = \frac{(4.42m/s)^{2} }{1.13m} = 17.3 m/s2 (3)[/tex]
2)
Once we got the value of a, applying Newton's 2nd law, we can find easily the net force on the bucket at the top of the circle, as follows:[tex]F_{net} = m*a = 2.17 kg * 17.3 m/s2 = 37.5 N (4)[/tex]
3)
We have already said, that at the top of the circle, the net force is just the sum of the tension T and the force of gravity, as follows:[tex]F_{net} = T + m*g = 37.5 N (5)[/tex]
Replacing m and g by their values, we can solve (4) for T:[tex]T = 37.5 N - m*g = 37.5 N - (2.17kg*98m/s2) \\ = 37.5 N - 21.3 N = 16.2 N (6)[/tex]
Albert Bandura emphasized the idea of __________, which is the belief one has in one’s own ability to succeed. A. operant conditioning B. determinism C. self-efficacy D. self-worth
Answer:
C
Explanation:
Albert Bandura emphasized the idea of Self efficacy which is the belief one has in one’s own ability to succeed.
What is Self efficacy?
A person's self-efficacy relates to their confidence in their ability to carry out the behaviors required to achieve particular performance goals (Bandura, 1977, 1986, 1997).
The belief in one's capacity to exercise control over one's own motivation, behavior, and social environment is known as self-efficacy. The goals for which people strive, the amount of effort put out to obtain goals, and the possibility of achieving particular levels of behavioral performance are all influenced by these cognitive self-evaluations.
Self-efficacy beliefs, unlike conventional psychological notions, are anticipated to change according to the operating domain and the environment in which an action occurs.
Therefore, Albert Bandura emphasized the idea of Self efficacy which is the belief one has in one’s own ability to succeed.
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Two bodies, A and B, have equal kinetic energies. The mass of A is nine times that of B. The ratio of the momentum of A to that of B is:_______.A. 1:9B. 1:3C. 1:1D.3:1E. 9:1
Answer:
D. 3 : 1
Explanation:
Let suppose that A and B are particles. From statement we know that [tex]K_{A} = K_{B }[/tex] (same kinetic energy) and [tex]m_{A} = 9\cdot m_{B}[/tex]. Then,
[tex]K_{A} = K_{B}[/tex]
[tex]\frac{1}{2}\cdot m_{A}\cdot v_{A}^{2} = \frac{1}{2}\cdot m_{B}\cdot v_{B}^{2}[/tex]
[tex]m_{A} \cdot v_{A}^{2} = m_{B}\cdot v_{B}^{2}[/tex]
[tex]\frac{v_{B}}{v_{A}} = \sqrt{\frac{m_{A}}{m_{B}} }[/tex]
[tex]\frac{v_{B}}{v_{A}} = 3[/tex]
And the ratio of the momentum of A to the momentum of B is:
[tex]r = \frac{m_{A}\cdot v_{A}}{m_{B}\cdot v_{B}}[/tex]
[tex]r = 9\times \frac{1}{3}[/tex]
[tex]r = 3[/tex]
Hence, the correct answer is D.
Which is an example of kinetic energy?
A. The energy stored in
ethanol
B. A ball sitting at the top of a ramp
C. A compressed spring
D. A hockey puck sliding across ice
D. A hockey puck sliding across ice
A ball whose mass is 1.8 kg is suspended from a spring whose stiffness is 8.5 N/m. The ball oscillates up and down with an amplitude of 13 cm. (a) What is the angular frequency
Answer:
The angular frequency of the ball is 2.173 rad/s.
Explanation:
Given;
mass of the ball, m = 1.8 kg
spring constant, k = 8.5 N/m
maximum displacement of the ball, A = 13 cm = 0.13 m
The angular frequency of the ball is calculated as;
[tex]\omega = \sqrt{\frac{k}{m} } \\\\\omega = \sqrt{\frac{8.5}{1.8}} \\\\\omega = 2.173 \ rad/s[/tex]
Therefore, the angular frequency of the ball is 2.173 rad/s.
Can any one help pls
Answer:
A and D are correct as they reduce GHG emissions while maintaining people's standard of living.
Answer:
Ig A and D
Explanation:
as :
a : Solar powered cars- redices emissions, relies on renewable sources and maintains current living.
d: a : WIND TURBINES - redices emissions, relies on renewable sources and is the closest to maintaining current living.
I hope im right !!!
Static Friction
Now let’s examine the static case. Remain on the “Force graphs” tab at the top of the window. Make sure the box labeled “Ffriction” is checked at the left of the screen, this will allow us to measure to force of friction experienced by an object as it slides down the ramp.
Draw a free body diagram for an object sitting on the incline at rest, assuming the incline is at the maximum angle BEFORE the object starts to move. Be sure to include friction and stipulate whether it is kinetic or static.
solve the quadratic equation: 5x²-2x-25=0
550 nm light passes through a diffraction grating with 3000 lines per centimeter. The screen is 115 cm away from the grating. What is the distance (in cm) between the 2nd order bright fringe and the 2nd dark fringe?
Answer:
69.7 cm
Explanation:
What is the distance (in cm) between the 2nd order bright fringe and the 2nd dark fringe?
For a diffraction grating, dsinθ = mλ where d = grating spacing = 1/(3000 lines per cm) = 1/3000 × 100 m per line = 1/300000 m = 1/3 × 10⁻⁵ m, m = order of fringe and λ = wavelength of light = 550 nm = 550 × 10⁻⁹ m.
Also, tanθ = x/D where x = distance of nth order fringe from central maximum and D = distance of screen from grating = 115 cm = 1.15 m
Now sinθ = d/mλ, Since θ is small, sinθ ≅ tanθ
So, d/mλ = x/D for a second order bright fringe, m = 2.
So, d/2λ = x/D
x = dD/2λ
So, x =
For a dark fringe, we have
d/(m + 1/2)λ = x'/D where x' is the distance of the fringe from the central maximum.
For a second-order dark fringe, m = 2. So,
d/(2 + 1/2)λ = x'/D
d/(5/2)λ = x'/D
2d/5λ = x'/D
x' = 2dD/5λ
So, the distance (in cm) between the 2nd order bright fringe and the 2nd dark fringe is x" = dD/2λ - 2dD/5λ
x" = dD/10λ
Substituting the values of the variables into the equation, we have
x"= 1/3 × 10⁻⁵ m × 1.15 m/(10 × 550 × 10⁻⁹ m)
x" = 1.15/165 × 10² m
x" = 0.00697 × 10² m
x" = 0.697 m
x" = 69.7 cm
The distance (in cm) between the 2nd order bright fringe and the 2nd dark fringe 69.7 cm
What is difraction?Diffraction of light occurs when a light wave passes by a corner or through an opening or slit that is physically the approximate size of, or even smaller than that light's wavelength
For a diffraction grating, dsinθ = mλ
where,
d = grating spacing = 1/(3000 lines per cm) = 1/3000 × 100 m per line = 1/300000 m = 1/3 × 10⁻⁵ m,
m = order of fringe
λ = wavelength of light = 550 nm = 550 × 10⁻⁹ m.
Also, [tex]tan\theta=\dfrac{x}{D}[/tex]t where
x = distance of nth order fringe from central maximum
D = distance of screen from grating = 115 cm = 1.15 m
Now [tex]Sin\theta =\dfrac{d}{m\lambda}[/tex] , Since θ is small, sinθ ≅ tanθ
So, [tex]\dfrac{d}{m\lambda}=\dfrac{x}{D}[/tex]
for a second order bright fringe, m = 2.
So, [tex]\dfrac{d}{2\lambda}=\dfrac{x}{D}[/tex]
[tex]x=\dfrac{dD}{2\lambda}[/tex]
For a dark fringe, we have
[tex]\dfrac{d}{(m+\dfrac{1}{2})\lambda}=\dfrac{X'}{D}[/tex]
where x' is the distance of the fringe from the central maximum.
For a second-order dark fringe, m = 2. So,
[tex]\dfrac{d}{(m+\dfrac{1}{2})\lambda}=\dfrac{X'}{D}[/tex]
[tex]\dfrac{d}{ \dfrac{5}{2}\lambda}=\dfrac{X'}{D}[/tex]
[tex]X'=\dfrac{2dD}{5\lambda}[/tex]
So, the distance (in cm) between the 2nd order bright fringe and the 2nd dark fringe is
[tex]X''=\dfrac{dD}{2\lambda}-\dfrac{2dD}{5\lambda}[/tex]
[tex]X''=\dfrac{dD}{10\lambda}[/tex]
Substituting the values of the variables into the equation, we have
[tex]x''=\dfrac{1}{3\times10^{-5}}\times \dfrac{1.15}{10\times 550\times 10^{-9}}[/tex]x
x" = 0.00697 × 10² m
x" = 0.697 m
x" = 69.7 cm
Hence the distance (in cm) between the 2nd order bright fringe and the 2nd dark fringe 69.7 cm
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A student carries a backpack for one mile. Another student carries the same backpack for two miles
Compared to the first student, how much work did the second student do?
Answer:
Compared to the first student, the second student did twice as much work as the first student.
Explanation:
The work done by the first student will be equal to the Force exerted by the backpack on the student carrying it multiplied by one mile (Distance). The work done by the second student will be equal to the Force exerted by the backpack on the student carrying it multiplied by two miles (Distance).
You use a 160 cm plank to lift a large rock. If the rock is 20cm from the fulcrum, what is the plank’s IMA?
Answer:
IMA = 8
Explanation:
Given the following data:
Length of plank = 160cm
Length of resistance = 20cm
To find the ideal mechanical advantage (IMA);
[tex] IMA= \frac {length \; of \; effort}{length \; of \; resistance} [/tex]
[tex] IMA= \frac {160}{20} [/tex]
IMA = 8
Two particles, an electron and a proton, are initially at rest in a uniform electric field of magnitude 570 N/C. If the particles are free to move, what are their speeds (in m/s) after 47.6 ns?
Explanation:
Given that,
Two particles, an electron and a proton, are initially at rest in a uniform electric field of magnitude 570 N/C.
We need to find their speeds after 47.6 ns.
For electron,
The electric force is given by :
[tex]F=qE\\\\F=1.6\times 10^{-19}\times 570\\\\=9.12\times 10^{-17}\ N[/tex]
Let a be the acceleration of the electron. So,
F = ma
m is mass of electron
[tex]a=\dfrac{F}{m}\\\\a=\dfrac{9.12\times 10^{-17}}{9.1\times 10^{-31}}\\\\a=10^{14}\ m/s^2[/tex]
Let v be the final velocity of the electron. So,
v = u +at
u = 0 (at rest)
So,
[tex]v=10^{14}\times 47.6\times 10^{-9}\\\\v=4.76\times 10^6\ m/s[/tex]
For proton,
Acceleration,
[tex]a=\dfrac{9.12\times 10^{-17}}{1.67\times 10^{-27}}\\\\=5.46\times 10^{10}\ m/s^2[/tex]
Now final velocity of the proton is given by :
[tex]v=5.46\times 10^{10}\times 47.6\times 10^{-9}\\\\v=2598.96\ m/s[/tex]
Hence, this is the required solution.
What would we need to do to make an electromagnet strong enough to move cars and trains
Answer:
The combined magnetic force of the magnetized wire coil and iron bar makes an electromagnet very strong. In fact, electromagnets are the strongest magnets made. An electromagnet is stronger if there are more turns in the coil of wire or there is more current flowing through it.
39. What is the change in momentum for a 5,000 kg ship in
outer space that experiences no net force over a 1 hr
period?
Answer:
Change in momentum is zero.
Explanation:
The following data were obtained from the question:
Mass (m) = 5000 kg
Time (t) = 1 h
Net force (F) = 0
Change in momentum =?
Force = Rate of change of momentum
0 = change in momentum
Change in momentum = 0
We can see from the above illustration that the net force is zero. Thus, the change in momentum is also zero.
Please help! quick and easy chart.
Answer:
sound and happiness are not matter
Explanation:
how many pennies can 4 folds of a paper hold?
A ball is thrown horizontally from the top of a 24.7 m building with a speed of 13.2m/s. Assuming level ground, the ball lands ___ m from the base of the building.
Answer:
The horizontal distance traveled by the ball is 29.7 m.
Explanation:
Given;
height of the building, h = 24.7 m
initial horizontal velocity, Vₓ = 13.2 m/s
The time taken for the ball to fall from the vertical height is calculated as;
[tex]h = V_yt + \frac{1}{2} gt^2[/tex]
where;
[tex]V_y[/tex] is initial vertical velocity = 0
[tex]h = 0 + \frac{1}{2} gt^2\\\\h = \frac{1}{2} gt^2\\\\t = \sqrt{\frac{2h}{g} } \\\\t = \sqrt{\frac{2\times 24.7}{9.8} } \\\\t = 2.25 \ s[/tex]
The horizontal distance traveled by the ball is calculated as;
[tex]X = V_x t\\\\X = 13.2 \times2.25\\\\X = 29.7 m[/tex]
Therefore, the horizontal distance traveled by the ball is 29.7 m.
⚠️I need help with the last question!⚠️
Answer:
I can't do your work for you but I can explain the last question;
The want you to tell them (In at least 3 sentences) Why you think your answers are correct or how your answer's match your hypothesis.
A hypothesis (for a little more help) is an idea or explanation that you then test through study and experimentation.
Outside science, a theory or guess can also be called a hypothesis. A hypothesis is something more than a wild guess but less than a well-established theory. Anyone who uses the word hypothesis is making a guess.
Explanation:
Sorry I didnt give you the exact answer but I hope this helps :)
The energy transformation a leaf on a tree undergoes when sunlight shines on it is an example of what?
Radiant to chemical
Mechanical to chemical
Electrical to mechanical
Chemical to radiant
1
2
3
4
5
Answer:Radiant to chemical
Explanation:
A freight train has a mass of [02] kg. The wheels of the locomotive push back on the tracks with a constant net force of 7.50 × 105 N, so the tracks push forward on the locomotive with a force of the same magnitude. Ignore aerodynamics and friction on the other wheels of the train. How long, in seconds, would it take to increase the speed of the train from rest to 80.0 km/h?
Answer:
t = 300.3 seconds
Explanation:
Given that,
The mass of a freight train, [tex]m=1.01\times 10^7\ kg[/tex]
Force applied on the tracks, [tex]F=7.5\times 10^5\ N[/tex]
Initial speed, u = 0
Final speed, v = 80 km/h = 22.3 m/s
We need to find the time taken by it to increase the speed of the train from rest.
The force acting on it is given by :
F = ma
or
[tex]F=\dfrac{m(v-u)}{t}\\\\t=\dfrac{m(v-u)}{F}\\\\t=\dfrac{1.01\times 10^7\times (22.3-0)}{7.5\times 10^5}\\\\t=300.3\ s[/tex]
So, the required time is 300.3 seconds.
If an object has a mass of 210g and the net force acting upon it is 5.0N, what is the acceleration of that object?
Answer:
24ms^-2 (2 sig figs)
Explanation:
F = ma
This means that the sum of all forces (or the net force) acting upon an object is equal to its mass x accelleration.
Its important to convert all parts of this equations in to SI units such that Force (N), Mass (kg) and Accelleration (ms^-2) to make sure that your answer is in the correct units.
F = ma so 5 = 0.21a
a = 5/0.21
a = 23.810 ms^-2 (5 sig figs)
What is cytoplasm in a animal cell?
Answer:
Cytoplasm is the jelly-like fluid that fills in all of the. space between the nucleus and the plasma membrane. All of the organelles within a cell are suspended in this fluid. The main function of the cytoplasm is to support the internal structures of the cell as well as maintaining shape and consistency of the cell.
Clouds
Clouds have a big influence on weather. They are a necessary precursor of precipitation, although not all of them
produce precipitation. Clouds also prevent some solar radiation from reaching the ground and absorb some of the
heat that is re-radiated from the surface. As a result, cloudy days are likely to be cooler and cloudy nights warmer
than clear days and nights.
Water vapor condenses out of the air when the temperature reaches the dew point. Air may reach its dew point
when humidity increases or air temperature decreases. The latter commonly happens when warm, moist air rises.
For clouds to form, water vapor must condense around tiny particles called nuclei (singular, nucleus). A nucleus
might be a speck of dust or smoke, or it might be a salt crystal. The condensation of many water molecules around
a nucleus forms a tiny droplet of liquid water. If billions of these water droplets come together, they make a cloud.
Clouds are classified in several ways. The most common classification used today divides clouds into groups based on altitude
• Middle clouds form at middle altitudes and consist of ice crystals, water droplets, or both. Examples of middle
clouds include altocumulus and altostratus clouds.
• Low clouds form at low altitudes and consist entirely or mainly of water droplets. Examples of low clouds
include stratus, stratocumulus, and nimbostratus clouds.
• Vertical clouds grow upward and have their bases at low altitude and their tops at middle or high altitude.
They form when strong air currents carry warm air upward. Examples of vertical clouds include cumulus and
nimbocumulus clouds.
Questions
1. How do clouds influence weather?
2. Explain how clouds form.
3. Outline how clouds are classified by altitude
Answer:
clouds from when moist, warm rising air cools and expands in the atmosphere. The water vapor in the air condenses to form tiny water droplets which are the basis of clouds.
Explanation:
Pick a small appliance in your home that you use regularly and look up on the internet how much power it operates at. Using the household voltage of 120 V, calculate the current flowing in this device. How much resistance would a resistor operating at that power and voltage have? If electricity costs $0.12/kWh, estimate how much you spend each month using this appliance. When you make your video, be sure to show the appliance you are talking about.
Answer:
Estimate money spent on the appliance( 9 Watt bulb ) on a monthly basis is $0.7776
Explanation:
Given the data in the question;
we are to pick a small appliance in our home that we use regularly and look up on the internet how much power it operates at;
so lets consider a 9 Watt bulb
Power p = 9 Watt
Household Voltage = 120 v
we know that; Power = Current I × Voltage V
so,
9 = I × 120
I = 9 / 120
I = 0.075 A
Resistance;
R = V / I
R = 120 / 0.075
R = 1600 Ω
Now, Energy consumed in 1 month(30 days) will be;
E = P × Τ
E = ( 9 / 1000kW ) × ( 30 × 24hrs )
E = 0.009 × 720 hrs
E = 6.48 kWh
Now, the cost for one month will be;
Cost = 6.48 × $0.12
Cost = $0.7776
Therefore, estimate money spent on the appliance( 9 Watt bulb ) on a monthly basis is $0.7776
Two identical conducting spheres are placed with their centers 0.30 m apart. One is given a charge of 12 X10^-9 C and the other is given a charge of -18 X 10^-9 C. a. Find the electric force exerted on one sphere by the other. b. The sphere are connected by a conducting wire. After equilibrium has occurred, find the electric force between the two spheres.
Answer:
Explanation:
Force between two charged conducting sphere
= k x Q₁ x Q₂ / r² , k is a constant Q₁ and Q₂ are charges and r is distance between them .
= 9 x 10⁹ x 12 x 10⁻⁹ x 18 x 10⁻⁹ / .30²
= 21600 x 10⁻⁹
= 2.16 x 10⁻⁵ N .
b )
After the spheres are joined together , there is redistribution of charge and remaining charge will be equally shared by them .
Charge on each sphere = (12 - 18 ) x 10⁻⁹ / 2
= - 3 x 10⁻⁹ C .
Force = 9 x 10⁹ x 3 x 10⁻⁹ x 3 x 10⁻⁹ / .30²
= 900 x 10⁻⁹ N .
is it possible for an atom to lose a proton and have a negative charge?
explain
Answer:
Sometimes atoms gain or lose electrons. The atom then loses or gains a "negative" charge. These atoms are then called ions. Positive Ion - Occurs when an atom loses an electron negative charge it has more protons than electrons.
Explanation:
:)
Derase
An electric heater Consumes 1.8 MJ When connected to a 250V supply for 30 minutes. Find the power rating of the heater and the current taken from the supply
Answer:
a. Power = 1000 Watts or 1 Kilowatts.
b. Current = 4 Amperes.
Explanation:
Given the following data;
Energy consumed = 1.8MJ = 1.8 × 10^6 = 1800000 Joules
Voltage = 250V
Time = 30 minutes to seconds = 30 * 60 = 1800 seconds
To find the power rating;
Power = energy/time
Substituting into the equation, we have;
Power = 1800000/1800
Power = 1000 Watts or 1 Kilowatts.
b. To find the current taken from the supply;
Power = current * voltage
1000 = current * 250
Current = 1000/250
Current = 4 Amperes.
The current flow in the light bulb is 0.5A
a.Calculate the amount of electric charge that flow through the bulb in 2 hour
b.If one election carries a
charge 1.6 x 10-14 c Find the number of election through the bulb in 2 hour?
Answer:
Explanation:
Given that,
The current in the light bulb, I = 0.5 A
(a) We know that,
Electric current = charge/time
or
Q = It
Put t = 2 hours = 7200 s
So,
Q = 0.5 × 7200
Q = 3600 C
(b) Charge on one electron, [tex]Q=1.6\times 10^{-19}\ C[/tex]
Let there are n electrons flow through the bulb in 2 hours.
I = Q/t
Since, Q = ne
So,
I = ne/t
[tex]n=\dfrac{I\times t}{e}\\\\n=\dfrac{0.5\times 7200}{1.6\times 10^{-19}}\\\\n=2.25\times 10^{22}[/tex]
Hence, this is the required solution.
Assume all of the resistors in the following circuits have a value of 5 ohms. Which ammeter will have the highest
reading?
Answer:
Circuit B
Explanation:
To know the correct answer to the question, we shall determine the reading of the ammeter i.e the current in each circuit. This can be obtained as follow:
For circuit A:
Resistance (R) = 5 ohms
Voltage (V) = 1.5 V
Current (I) =?
V = IR
1.5 = I × 5
Divide both side by 5
I = 1.5 / 5
I = 0.3 A
For circuit B:
We'll begin by calculating the total resistance in the circuit. This can be obtained as follow:
Resistance 1 (R₁) = 5 ohms
Resistance 2 (R₂) = 5 ohms
Total resistance (Rₜ) =?
Since they are in parallel connections, the total resistance can be obtained as illustrated below:
Rₜ = R₁ × R₂ / R₁ + R₂
Rₜ = 5 × 5 / 5 + 5
Rₜ = 25 / 10
Rₜ = 2.5 ohms
Finally, we shall determine the current in the circuit.
Resistance (R) = 2.5 ohms
Voltage (V) = 1.5 V
Current =?
V = IR
1.5 = I × 2.5
Divide both side by 2.5
I = 1.5 / 2.5
I = 0.6 A
For circuit C:
We'll begin by calculating the total resistance in the circuit. This can be obtained as follow:
Resistance 1 (R₁) = 5 ohms
Resistance 2 (R₂) = 5 ohms
Total resistance (Rₜ) =?
Since they are in series connections, the total resistance can be obtained as illustrated below:
Rₜ = R₁ + R₂
Rₜ = 5 + 5
Rₜ = 10 ohms
Finally, we shall determine the current in the circuit.
Resistance (R) = 10 ohms
Voltage (V) = 1.5 V
Current =?
V = IR
1.5 = I × 10
Divide both side by 10
I = 1.5 / 10
I = 0.15 A
SUMMARY:
Circuit >>>>>>> Current
A >>>>>>>>>>>> 0.3 A
B >>>>>>>>>>>> 0.6 A
C >>>>>>>>>>>> 0.15 A
from the above calculations, circuit B has the highest ammeter reading.
The temperature of an object is
A. The average kinetic energy of its atoms and molecules
B. The total potential and kinetic energy of its atoms and molecules
C. The transfer of kinetic energy from one place or object to another through collisions between atoms and molecules
A cat is sleeping on the floor in the middle of a 2.8-m-wide room when a barking dog enters with a speed of 1.40 m/s. As the dog enters, the cat (as only cats can do) immediately accelerates at 0.85 m/s2 toward an open window on the opposite side of the room. The dog (all bark and no bite) is a bit startled by the cat and begins to slow down at 0.10 m/s^2 as soon as it enters the room.
Required:
How far is the cat in front of the dog as it leaps through the window?
Answer:
the cat is 0.4238 m in front of the dog as it leaps through the window
Explanation:
Given that;
acceleration a = 0.85 m/s²
speed v = 1.40 m/s
the cat is at rest, so initial velocity u = 0
we know that, since the cat is sleeping on the floor in the middle of a 2.8-m-wide room, it needs to cover (2.8 m / 2 ) distance to get to the window;
using the second equation equation of motion;
s = ut + 1/2 at²
we substitute
2.8/2 = 0×t + 1/2 × 0.85 × t²
1.4 = 0.425t²
t = √( 1.4 / 0.425 )
t = 1.81497 sec
now, at acceleration 0.10 m/s²
the dog has to cover the distance;
s = ut + 1/2 at²
s = ( 1.4 × 1.81497) - 1/2 × 0.10 × 1.81497²
s = 2.540958 - 0.1647
s = 2.3762 m
The cant in front of the dog as it leaps through the window;
distance = 2.8 m - 2.3762 m
distance = 0.4238 m
Therefore, the cat is 0.4238 m in front of the dog as it leaps through the window