Answer:
θ = 47.75º East of North.
Explanation:
Assuming no external forces acting during the collision, total momentum must be conserved.Since momentum is a vector, if we project it along E-W and N-S axes, the momentum components along these axes must be conserved too.So, for the N-S axis, we can write the following equation:[tex]p_{Northo} = p_{Northf} (1)[/tex]
Since the car moving due east has no speed component along the N-S axis, the initial momentum along this axis is simply:[tex]p_{Northo} = m_{1} * v_{1o} (2)[/tex]
where m₁ = 1570 kg, v₁₀ = 156 km/h
In order to work with the same units, we need to convert the speed in km/h to m/s, as follows:[tex]v_{1o} = 156 km/h *\frac{1000m}{1 km}*\frac{1h}{3600s} = 43.3 m/s (3)[/tex]
Replacing by the values in the left side of (1), we get:[tex]p_{Northo} = m_{1} * v_{1o} = 1570 kg* 43.3 m/s = 67981 kg*m/s (4)[/tex]
Since the collision is inelastic, both cars stick together, so we can write the right side of (1) as follows:[tex]p_{Northf} = (m_{1} + m_{2})* v_{fNorth} = 3815.1 kg* v_{fNorth} (5)[/tex]
From (4) and (5) , we can solve for VfNorth:[tex]V_{fNorth} = \frac{67981kg*m/s}{3815.1kg} = 17.8 m/s (6)[/tex]
We can repeat exactly the same process for the E-W axis:[tex]p_{Easto} = p_{Eastf} (7)[/tex]
Since the car moving due north has no speed component along the E-W axis, the initial momentum along this axis is simply:[tex]p_{Easto} = m_{2} * v_{2o} (8)[/tex]
As we did with v₁₀, we need to convert v₂₀ from km/h to m/s, as follows:[tex]v_{2o} = 120 km/h *\frac{1000m}{1 km}*\frac{1h}{3600s} = 33.3 m/s (9)[/tex]
Replacing by the values in the left side of (7), we get:[tex]p_{Easto} = m_{2} * v_{2o} = 2245.1 kg* 33.3 m/s = 74762 kg*m/s (10)[/tex]
Since the collision is inelastic, both cars stick together, so we can write the right side of (7) as follows:[tex]p_{Eastf} = (m_{1} + m_{2})* v_{fEast} = 3815.1 kg* v_{fEast} (11)[/tex]
From (10) and (11) , we can solve for VfEast:[tex]V_{fEast} = \frac{74762 kg*m/s}{3815.1kg} = 19.6 m/s (12)[/tex]
In order to find the angle East of North of the velocity vector, as we know the values of the horizontal and vertical components, we need just to apply a little bit of trigonometry, as follows:[tex]tg \theta = \frac{V_{fEast}}{V_{fNorth} } = \frac{19.6}{17.8} = 1.1 (13)[/tex]
The angle θ, East of North, is simply tg⁻¹ (1.1):θ = tg⁻¹ (1.1) = 47.75º E of N.
Determine a differential equation for the velocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity. Assume the downward direction is positive. (Use k > 0 for the constant of proportionality, g > 0 for acceleration due to gravity, and v for v(t).)
A freely falling mass m will be pulled down toward the ground with downward acceleration +g while feeling upward drag D due to air resistance with acceleration -a such that D = - m a = - k v ². Hence the body's velocity v(t) changes with respect to time t according to the differential equation,
dv(t)/dt = m g - k v ²
Can a golf ball bounce like a rubber ball? Due in 1 hour. 15 points.
Answer:
So, I tested it out and came to a conclusion.
The rubber ball is quite bouncy due to the fact that it is made of rubber which is what makes it bounce back and high, but although the golfball does in fact bounce back it does not bounce as high as the rubber ball due to the fact that it is made of plastic.
Explanation:
Hope this helps you out!
all igneous rock forms from cooling lava, but not all of them look the same, (ex: some have large crystals) why is that:
a. lava cooled BENEATH the surface and SLOWLY allows large crystals to develop bc they have more time to grow in size.
b. lava cooled ABOVE the surface which SLOWLY allows large crystals to develop bc they have more time to grow in size.
c. lava cooled BENEATH the surface and QUICKLY allows large crystals to develop bc they have more time to grow in size.
D. lava cooled ABOVE the surface which QUICKLY allows large crystals to develop bc they have more time to grow in size.
Answer:
b
Explanation:
Find the required answer to the following by substituting the numbers. (Bonus points for knowing the units). PLEASE ANSWER
a) Using Fnet = ma, what is Fnet if m = 13.2kg and a = 10ms^-2?
b) Using I = P/V, what is I if V = 15V and P = 75W
Answer:
a) F=ma
F=13.2×10
F=132
b) I=P/V
I=75/15
I=5
with which of the following is the weak nuclear force associated
Determine the small gravitational force F which the copper sphere exerts on the steel sphere. Both spheres are homogeneous, and the value of r is 65 mm. Express your result as a vector.
Answer:
[tex]F=3.665 \times 10^{-7} N[/tex] acting along the line joining both the sphere and always attractive in nature.
Explanation:
The given radius of both the sphere, r= 65 mm = 0.065 m
So, the volume of the spheres, [tex]v= \frac 4 3 \pi r^3[/tex]
[tex]v= \frac 4 3 \pi (0.065)^3 = 1.150 \times 10^{-3} m^3[/tex]
The density of steel, [tex]\rho _s = 7850 kg/m^3[/tex]
and the density of copper, [tex]\rho_c= 8940 kg/m^3[/tex]
Let M be the mass of the copper ball and m is the mass of the steel ball.
So, [tex]M=\rho_c v= 8940\times 1.150 \times 10^{-3} = 10.281[/tex] kg
[tex]m=\rho_s v= 7850\times 1.150 \times 10^{-3} = 9.0275[/tex] kg
The gravitational force, F, between the two objects having masses M and m and separated by distance d is
[tex]F=\frac{GMm}{d^2}[/tex]
Where [tex]G= 6.674 30 x 10^{-11} m^3 kg^{-1} s^{-2}[/tex] is the universal gravitational constant.
When both the sphere touches each other, d = 2r= 2 x 0.065 = 0.13 m
Hence, the gravitational force between both the sphere,
[tex]F= \frac {6.674 30 x 10^{-11}\times 10.281 \times 9.0275}{0.13^2} \\\\F=3.665 \times 10^{-7} N[/tex]
The nature of gravitational force is always attractive and acting along the line joining the center of both the sphere.
who was the first president of America
Answer:George Washington
Explanation:On April 30, 1789, George Washington, standing on the balcony of Federal Hall on Wall Street in New York, took his oath of office as the first President of the United States.
Answer:
George Washington
Explanation:
Hope this helps out
1
A boy pulls his toy on a smooth horizontal
surface with a rope inclined at 60° to the
horizontal. If the effective force pulling the toy
along the horizontal surface is 5 N, calculate
the tension in the rope:
A 2.50 N B 4.33 N C 5.00 N
D 8.66 N E 10.0 N.
(SC/GCE)
Answer: wqcjn qefveqeqfbj qeib
Explanation:oiaer vgneiofrvn eiforbnewtjbioe
The rate of change of work with respect to time is called
1) power
2) momentum
3) energy
4)force
Answer:
Power
Explanation:
Power, by definition, is the rate of doing work (aka, work with respect to time).
3 A picture is supported by two vertical strings; if the weighi
of the picture is 50 N what is the force exerted by each
string ?
Answer:
The force exerted by each string is 25 N
Explanation:
Net Force
The net force is the vector sum of forces acting on a body. The net force is a single force that represents the effect of the original forces on the body's motion. It gives the particle the same acceleration as all those actual forces together as described by Newton's second law of motion.
The picture described in the problem is hanging at rest supported by two vertical strings. This means that the net force acting on it is zero.
Assume the magnitude of each of these equal forces is F, and the picture has a weight of W=50 N, thus the net force is:
F + F - W
The positive signs indicate an upwards direction and the negative sign means a downwards direction. Since the net force is zero:
F + F - W = 0
2F = W
F = W/2 = 50 N/2
F = 25 N
The force exerted by each string is 25 N
need help asap.......................
Answer:
vt3bryhtevy4g24vu5hy4
You decide to do an experiment to investigate Newton's Third Law. Below are several
example experiments you might run to help investigate your questions. Which one of the
following examples below are not related to Newton’s Third Law?
A. You and a friend push on each other’s hands while wearing roller blades and
observe the force of the shove.
B. You set a ball on the ground and observe the force of gravity on the ball
C. You stand on the bathroom scale and then decide to jump off and observe the
change in the reading.
D. You drive a remote-controlled car and observe the force at work
Answer:
C
Explanation:
You stand on the bathroom scale and then decide to jump off and observe the
change in the reading.
A man rides a bicycle that is connected to an electrical generator. If he rides as hard as he can, his body can produce a mechanical power of 500 W, but the generator is only 40% efficient at converting mechanical energy into electrical energy.How many 100 W incandescent light bulbs can he power
Answer: the man can power 2 incandescent light bulbs
Explanation:
Given that;
power produced by the body while riding = 500 W
Efficiency of generator = 40% = 0.4
First we need to convert the mechanical energy to electric energy;
which efficiency of generator multiply by power input, so
⇒ 0.4 × 500 = 200 W
Now, if 1 incandescent light bulbs is 100 W
x incandescent light bulbs bulbs is 200 W
100x W= 200 W
x = 200 W / 100 W
x = 2
Therefore, the man can power 2 incandescent light bulbs
A soccer player kicks a soccer ball (m = 0.42 kg) accelerating from rest to 32.5m/s in 0.21s. Determine the force that sends soccer ball towards the goal.
Plis I need Help:(
Answer:
F=65 N
Explanation:
Uniform Acceleration
When an object changes its velocity at the same rate, the acceleration is constant.
The relation between the initial and final speeds is:
[tex]v_f=v_o+a.t[/tex]
Solving for a:
[tex]\displaystyle a=\frac{v_f-v_o}{t}[/tex]
Where:
vf = Final speed
vo = Initial speed
a = Constant acceleration
t = Elapsed time
The ball is kicked from rest vo=0 to vf=32.5 m/s in t=0.21 s. Computing the acceleration:
[tex]\displaystyle a=\frac{32.5-0}{0.21}[/tex]
[tex]a=154.8\ m/s^2[/tex]
Note: We have shown this result rounded to the nearest tenth, but we kept all the decimals in a scientific calculator for further calculations.
The force needed to accelerate the soccer ball is calculated by:
F = ma
The ball has a mass of m=0.42 kg, thus:
F=0.42*154.8
F=65 N
As mentioned, this result can only be obtained by keeping full precision in the above calculations.
1. the position of a particles moving on a straight line is given by X =12 + 18t + 9t^2meter
(a) find the instantaneous veloctiy at
t=5s [dx/dt=v]
Answer:
v = 108 m/s.
Explanation:
Given that,
The position of a particle moving on a straight line is given by :
[tex]X =12 + 18t + 9t^2[/tex]
We need to find the instantaneous velocity at t=5s.
Velocity, [tex]v=\dfrac{dX}{dt}[/tex]
So,
[tex]v=\dfrac{d(12 + 18t + 9t^2)}{dt}\\\\=18+18t[/tex]
Instantaneous velocity at t = 5 s will be :
v = 18+18t
v = 18+18(5)
= 18 + 90
= 108 m/s
So, the instantaneous veloctiy at t=5s is 108 m/s.
a 13-gram bullet, moving at 270 m/s, penetrates a 2 kg block of wood and emerges at a speed of 130 m/s. if teh block sits one a fricitonless surface, find its velocity after the bullet emerges.
Answer:
1.52m/s
Explanation:
Using the law of conservation of momentum
m1u1 + m2u2 = (m1+m2)v
m1 and m2 are the masses
u1 and u2 are the initial velocities
v is the final velocity
Substitute the given values into the formula
0.013(270)+2(130) = (270+130)v
3.51+260 = 400v
263.51 = 400v
v = 400/263.51
v = 1.52m/s
Hence the velocity after the bullet emerges is 1.52m/s
Which of the following is NOT a characteristic of noble gases? *
very reactive
colorless
odorless
unreactive
Question 3 of 10
An engine performs 6400 J of work on a motorbike. The motorbike and rider
have a combined mass of 200 kg. If the bike started at rest, what is the speed
of the bike after the work is performed?
Answer:
8 m/s
Explanation:
KE Formula: KE = 1/2mv^2
Kinetic Energy is equal to energy, J.
6400 = 1/2 * 200 * V^2
1/2 * 200 = 100
6400 = 100 * V^2
6400/100 = V^2
64 = V^2
Square root both sides
Speed is 8 m/s
Why solar panels are usually painted black
Answer:
The silicon used to make monocrystalline solar cells has a high level of purity. ... Because of the way light interacts with a monocrystalline silicon layer, monocrystalline solar panels appear black in color.
the density of a glass is 2.5 g/cm3. if the glass breaks, what is the density of the smaller pieces
Answer:
See the explanation below.
Explanation:
Density will remain the same since density is the relationship between mass and volume. As we can see in the equation below.
[tex]Ro=m/V[/tex]
where:
Ro = density = 2.5 [g/cm³]
m = mass [g]
V = volume [cm³]
In such a way that when the glass is broken the small fragments retain the same density ratio. That is, each fragment has a small mass and a small volume. That's why the density remains the same.
i need help if u see this don't skip
Answer:
i didnt skip because you said not to ion even know the answer tho
Explanation:
Answer:
Na connect with chlorine because sodium is a cation that is in the alkali metal group. Sodium has a +1 charge and all it needs to do is lose a electron to become stable. This is is since Na only has one valence electron and to create a bond, it has no choice but to lose a electron. In the alkali metal group, they are the groups that are the most reactive metals. On the other hand, chlorine is a anion that is in the halogens group. So chlorine has a -1 charge and all it needs to do is gain a electron to become stable. This is since chlorine has 7 valance electrons and needs 1 more electron to have a full outer shell. In the halogens group, they are the groups that are the most reactive nonmetals. When sodium and chlorine create a chemical bond, they create a charge of 0 which is neutral. That's why they would connect to create a substance that is part of everything we eat.
1(-1 )+ 1(1) = 0.
Explanation:
Hope it helped!
Which ray diagram demonstrates the phenomenon of absorption?
Answer:
B
Explanation:
The ray diagram demonstrated the phenomenon of absorption in B. Hence, option B is correct.
What is absorption?Absorption is the phenomenon of electromagnetic radiation taking up the energy of photons and it also transfers the electromagnetic energy to the internal energy of the absorber.
Absorption refers to the transfer of the energy of a wave to matter as the wave passes through it. The process in which the light waves get converted into energy. Absorption causes attenuation of the waves and the intensity decreases gradually when the light waves propagate through the medium.
From the given, the first diagram represents the light passes through the slit, it gets diffracted and forms alternate bright and dark fringes in the screen. The third diagram represents that the light ray strikes the surface it gets reflected and the path of light gets changed.
Thus, the absorption is the ray diagram given in the second image. Hence, option B is correct.
To learn more about Wave interactions:
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Which of the following is a pure substance?
What happens to the molecules of a substance when it changes phase?
When it comes to phase shifts or phase change the greater the intermolecular interactions are the closer the molecules are to one another.
What is phase change?A phase change occurs when matter transitions from one state to another (solid, liquid, gas, plasma). When enough energy is provided to the system (or when a significant quantity is removed), as well as when the pressure on the system is adjusted, these changes occur.Any two phases of matter can undergo phase transitions.All phase shifts are accompanied by an energy shift.Isothermal phase shifts occur in all cases.Temperature changes can cause substances to change phase often. Most substances are solid at low temperatures; as the temperature rises, they become liquid; and at even higher temperatures, they become gaseous.To Know more about Phase change here
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Calculate the increase in the internal energy when 1000 g of boiling water at 212° F is converted into steam at the same
temperature. Atmospheric pressure is 1.013 X 10 Pa and the latent heat of vaporization is 2.260 MJ kg
-1
Answer:
The increase in the internal energy is 1.840 x 10⁶ J.
Explanation:
Given;
mass of the water, m = 1000 g = 1 kg
temperature of the boiling water, t = 212 ° F = 100 ° C
latent heat of vaporization, L = 2.260 MJ/kg = 2.260 x 10⁶ J/kg
The internal energy of the boiling water is calculated as;
Q₁ = mcΔθ
where;
c is specific heat capacity of water, = 4200 J/kg.⁰C
Δθ is change in temperature = 100 ° C
Q₁ = 1 x 4200 x 100
Q₁ = 420,000 J
The internal energy of the vaporized steam is calculated as;
Q₂ = mL
Q₂ = 1 x 2.260 x 10⁶
Q₂ = 2,260,000 J
The increase in the internal energy is calculated as;
ΔQ = Q₂ - Q₁
ΔQ = 2,260,000 J - 420,000 J
ΔQ = 1,840,000 J
ΔQ = 1.840 x 10⁶ J
Therefore, the increase in the internal energy is 1.840 x 10⁶ J.
A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 4.0 m/s, skates by with the puck. After 2.80 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 0.14 m/s2, determine each of the following:
a. How long does it take him to catch his opponent?
b. How far has he traveled in that time?
Answer:
a)[tex]t=59.817652833125294s \approx 59.8s[/tex]
b)[tex]D_1=894.01m[/tex]
Explanation:
From the question we are told that
Speed of opposing player [tex]V_2=4.0m/s[/tex]
First player chase his opponent after[tex]t=2.80t[/tex]
Acceleration of first player [tex]a=0.14 m/s2[/tex]
Let time of catch be [tex]t_c[/tex]
a)Generally the Equation for distance covered is mathematically given as follows
Distance to catch First opponent
[tex]D_1=\frac{1}{2}(0.14)t^2[/tex]
[tex]D_1=0.07t^2[/tex]
Distance to covered Second opponent
[tex]D_2=(2.8+t)*4[/tex]
Generally when first opponent catch the second opponent it is represented mathematically as
[tex]D_2=D_1[/tex]
[tex]0.07t^2=(2.8+t)*4[/tex]
[tex]0.07t^2=11.2+4t[/tex]
[tex]0.07t^2-4t-11.2[/tex]
[tex]t=59.817652833125294s \approx 59.8s[/tex]
b)Generally the the total time traveled by the first opponent is mathematically given as
[tex]D_1=\frac{t^2}{4}[/tex]
[tex]D_1=\frac{59.8^2}{4}[/tex]
[tex]D_1=894.01m[/tex]
What may result when the energy that builds up at plate boundaries is released because the plates suddenly overcome the force of friction?
volcano
hot spot
earthquake
trench
Suppose the entire population of the world gathers in one spot and, at the sounding of a prearranged signal, everyone jumps up. While all the people are in the air, does Earth gain momentum in the opposite direction?
a) No; the inertial mass of Earth is so large that the planet’s change in motion is imperceptible.
b) Yes; because of its much larger inertial mass, however, the change in momentum of Earth is much less than that of all the jumping people.
c) Yes; Earth recoils, like a rifle firing a bullet, with a change in momentum equal to and opposite that of the people.
d) It depends.
Answer:(B)
Explanation:
No; the inertial mass of Earth is so large that the planet’s change in motion is imperceptible, therefore the correct answer is option A.
What is Newton's first law?According to Newton's first law, until pushed to alter its condition by the intervention of an external force, every object will continue to be at rest or in uniform motion along a single direction.
As given in the problem suppose the entire population of the world gathers in one spot and, at the sound of a prearranged signal, everyone jumps up. While all the people are in the air, we have to find out if Earth gains momentum in the opposite direction,
The mass of the earth is very huge approximately 5.97 ×10²⁴ kilogram.
Even the combined mass of all the population combined would be negligible as compared to the mass of the earth.
Thus, the earth would not gain momentum in the opposite direction.
Learn more about Newton's First Law here;
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A 365-kg car traveling horizontally at 21.1 m/sec slams into a tree and comes to a halt in 0.22 seconds. What force did the tree exert on the car to stop it?
please show work
Explanation:
Remember Newton's Second law
[tex]F = ma[/tex]
We can use this to solve for the force exerted by the tree on the car when it stops the car.
We aren't given the acceleration directly in the problem statement, but we can solve for acceleration.
Recall that acceleration is the change is velocity per unit time. [tex]a = \frac{\Delta v}{\Delta t}[/tex]
We know the original velocity as 21.1 m/s and the final velocity as 0.0 m/s. The time that it takes to stop the car is 0.22 seconds.
Now we can solve using the equation. [tex]F = \frac{21.1 - 0.0}{0.22} * 365[/tex]
An electric eel develops a 450 V potential difference between its head and tail. The eel can stun a fish or other prey by using this potential difference to drive a 0.80 A current pulse for 1.0 ms. What are (a) the energy delivered by this pulse and (b) the total charge that flows
Answer:
(a) The energy delivered by the pulse is 0.36 J
(b) the total charge that flows is 0.8 mC
Explanation:
Given;
potential difference of the electric eel, V = 450 V
current flow, I = 0.8 A
time of current flow, t = 1.0 ms = 1.0 x 10⁻³ s
(a) The energy delivered by the pulse is calculated as;
E = Pt
where;
t is time
P is power developed = IV
E = (IV)t
E = IVt
where;
I is the current
V is the potential difference
E = 0.8 x 450 x 1.0 x 10⁻³
E = 0.36 J
(b) the total charge that flows is calculated as;
Q = It
where;
I is the current
t is the time
Q = 0.8 x 1.0 x 10⁻³
Q = 0.0008 C
Q = 0.8 mC.
