Addition of vectors:
vector u
has a magnitude of 20 and a direction of 0º with respect to the horizontal, vector v has a magnitude of 40 and a direction of 60º with respect to the horizontal.
a) Find the magnitude and direction of the resultant to the nearest whole
number.
Vector Sum:
The resultant of two vectors is simply the vector sum of the vectors. There are a handful of ways to present the resultant factor; the notation that shows the vector magnitude and direction is called the polar vector notation. An example of a vector presented in polar vector notation is
a∠θ where a is the magnitude and θis the angle that the vector makes with the horizontal axis.
Answer and Explanation:
Let's first present the vectors in rectangular vector notation.
For the vector →u of magnitude 20 and direction 0∘ to the horizontal axis, the vector is →u=^i20.
For the vector →v
of magnitude 40 and direction 60∘ to the horizontal axis, the vector is →v=^i40cos60∘+^j40sin60∘.
The resultant vector →w is the vector sum of the vectors, i.e.
→w=→u+→v
=^i20+^i40cos60∘+^j40sin60∘
=^i(20+40cos60∘)+^j(40sin60∘)
=^i40+^j20√3
For a vector ^ix+^jy, the magnitude of the vector is √x2+y2 and the direction above the horizontal axis is θ=tan−1(yx).
Let's use the formulas:
|→w|∠θ=√(40)2+(20√3)2∠tan−1(20√340)≈52.9∠40.9∘
The magnitude of the vector is about 53 units in the direction 41-degrees above the horizontal axis.
The magnitude of the resultant vector would be 60 units, and its direction will be 0°.
To find the magnitude and direction of the resultant vector when adding vectors u and v, we can use vector addition formulas:
Magnitude of the Resultant Vector (R):
R = √(u^2 + v^2 + 2uv * cosθ)
where:
u = magnitude of vector u (20)
v = magnitude of vector v (40)
θ = angle between vectors u and v (60°)
Plugging in the values:
R = √(20^2 + 40^2 + 2 * 20 * 40 * cos(60°))
≈ √(400 + 1600 + 1600)
≈ √3600
= 60
Direction of the Resultant Vector (θR):
Use the Law of Cosines to find the angle θR between the resultant vector R and vector u:
cosθR = (v^2 + R^2 - u^2) / (2 * v * R)
Plugging in the values:
cosθR = (40^2 + 60^2 - 20^2) / (2 * 40 * 60)
= (1600 + 3600 - 400) / 4800
= 1
Since cos(0°) = 1, we have θR = 0°.
So, the magnitude of the resultant vector is 60 units, and its direction is 0°.
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A force of 20 N acts upon a 5 kg biock. Calculate the acceleration of the object.
Answer:
F=ma
Explanation:
Given required solution
F=20N a=? a=F/m
m=5kg a=20/5
a=4m/s^2
What is the relationship between the temperature of a star and its luminosity?
5. What must occur for an object to exert a contact force on another object?
Answer:
An object must be touching another.
a ball is thrown vertically down from the edge of a cliff with a speed of 5.2m/s how high is the cliff if it took 11s for the ball to reach the ground
[tex]\\ \sf\longmapsto h=ut+\dfrac{1}{2}gt^2[/tex]
[tex]\\ \sf\longmapsto h=5.2(11)+\dfrac{1}{2}(9.8)(11)^2[/tex]
[tex]\\ \sf\longmapsto h=57.2+4.9(121)[/tex]
[tex]\\ \sf\longmapsto h=57.2+592.9[/tex]
[tex]\\ \sf\longmapsto h=650.1m[/tex]
Given a table of values for the exponential function f(x) and a description of the
transformation for the function g(x)
, fill out the table of values based on the original
points for glx), the transformed function.
- 1
0
2
16
3
Reflect over
0
2
4
0-4, -1, -12
1
16
.
64
01, 1, 4, 16, 64
,
4, 1, , 162
0-1, -1, –4, – 16, – 64
Answer:its D
Explanation:
i did the test and got it right
The transformation function of the given exponential function is -1/4, -1, -4, -16, -64. Hence option D is correct.
What is an exponential function?An exponential function is a mathematical relation to find exponential growth or decay for the given data. It represents the constant change in independent variables and gives the same proportional change.
The exponential function is expressed as f(x) = exp (x) or eˣ where x is variable and e is constant which is called the base of the equation.
From the given,
the exponential function f(x) = 1/4, 1,4,16,64
The transformation function G(x) is the inverse of the exponential function and is equal to -1/4,-1, -4,-16,-64.
Hence, the ideal solution is option D.
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Need an answer in Meters
Answer:
• let's first get time
[tex]{ \rm{s = ut + \frac{1}{2}g {t}^{2} }} \\ \\ { \rm{78.4 = 30t + 5 {t}^{2} }} \\ \\ { \rm{ {t}^{2} + 6t - 15.68 = 0}} \\ \\ { \rm{time \approx \: 2 \: seconds}}[/tex]
• let's find horizontal displacement
[tex]{ \rm{s = ut + \frac{1}{2}g {t}^{2} }} \\ \\ { \rm{s = (30 \times 2) \times ( \frac{1}{2} \times 0 \times {2}^{2}) }} \\ \\ { \rm{displacement = 60 \: meters}}[/tex]
g is acceleration due to gravity [ vertically: g is 10 m/s². horizontally: g is 0 ]To hit a fish that he sees beneath the water, where should he aim?
Ok I guess you are gonna use arrow/spear. Ok so what I learned is that the best place to hit and fish is the gills or the eye(s) because without the gills fish won't be able to breath.If you hit it on the eye it will take a while to kill the fish.The fish will feel lots of pain and start swim like crazy and probably go away.So i will say the BEST way to kill a fish to to hit it's gills.
In case you don't have any materials to kill fish:
IF you are in the wild with fish and you don't have a hook,spear,arrow, etc. I will recommend you to use a rock that his big but easy to grip.Hit the fish on top of its head just behind the eyes.Or get a stick no too thick or too skinny just like between those and start whittle it to a arrow then aim and shoot.
Hope this helps! =D
What is final velocity
Answer:
Final velocity is the velocity which the body has at the end of the given time period.
a physics student throws a stone horizontally off a cliff. one second later, he throws a second identical stone in exactly the same way. which of the following statements is true?
The second stone hits the ground exactly one second after the first.
The distance traveled by each stone down the cliff is calculated using second kinematic equation;
[tex]h = v_0_yt + \frac{1}{2} gt^2[/tex]
where;
t is the time of motion [tex]v_0_y[/tex] is the initial vertical velocity of the stone = 0[tex]h = \frac{1}{2} gt^2[/tex]
The time taken by the first stone to hit the ground is calculated as;
[tex]t_1 = \sqrt{\frac{2h}{g} }[/tex]
When compared to the first stone, the time taken by the second stone to hit the ground after 1 second it was released is calculated as
[tex]t_2 = \sqrt{\frac{2h}{g} } + 1[/tex]
[tex]t_2 = t_1 + 1[/tex]
Thus, we can conclude that the second stone hits the ground exactly one second after the first.
"Your question is not complete, it seems be missing the following information;"
A. The second stone hits the ground exactly one second after the first.
B. The second stone hits the ground less than one second after the first
C. The second stone hits the ground more than one second after the first.
D. The second stone hits the ground at the same time as the first.
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Li Wei loves cardio and finds it very easy to fit into his schedule. Because he knows it is important to diversify his exercise routine, sometimes he runs and other days he rides his bike. What else should Li Wei consider regarding his routine?
OPTIONS:
A.
He should add some strength training.
B.
He needs to add one more form of cardio.
C.
He has too much cardio and should cut half of it.
D.
His program works for him, so he should not change it.
PLEASE NO LINKS
Answer:
D.
Explanation:
Li Wei loves cardio and finds it very easy to fit into his schedule. Li Wei should consider his routine is his program works for him, so he should not change it. The correct option is D.
What is cardio?Any form of exercise that raises your heart rate and keeps it there for a long time is considered cardio. As you start to breathe more quickly and deeply, your respiratory system will start to work harder.
The four components of a fitness program are flexibility, cardio, strength, and power.
The physical exercise that increases muscular strength and fitness is referred to as strength.The capacity to produce the most muscle contractions possible during a movement is referred to as power.Cardio refers to the capacity to handle various circumstances of various lengths.Flexibility is the characteristic that is linked to the range of motion offered by a particular joint.Therefore, the correct option is D. His program works for him, so he should not change it.
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HOW WOULD SOUND REFLECT
Answer:
Reflection. If a sound is not absorbed or transmitted when it strikes a surface, it will be reflected. ... Reflection of a sound wave at a barrier, as if from an imaginary source at an equal distance behind the barrier. Sound reflection gives rise to DIFFUSION, REVERBERATION and ECHO.
Answer:
by a echo
Explanation:
if u are I a sound proof room you shout to the wall the echo will then reflect
In induction, what charge does a neutral substance gain compared to the object brought near it?
Explanation:
In induction, what charge does a neutral substance gain compared to the object brought near it?
The neutral object gains the same type of charge as the object that touched it because the electrons move from one object to the other (Figure 10.16). Induction is the movement of electrons within a substance caused by a nearby charged object, without direct contact between the substance and the object.
The charge gained by the neutral substance, gained compared to the object brought near it, had the same kind of charge that was present when it touched it.
What is induction?The alteration of the distribution of electric charge on a substance is caused by the effect of induction. A negatively charged object brought close to an electrically neutral object causes a positive charge on the near side and a negative charge on the far side of the neutral object as a result of the electric force between charged particles that make up materials.
This very little polarization, or separation of charge, lessens the electric field inside the dielectric.
Because the electrons go from one thing into the next, the neutral object acquires the same kind of charge that was present when it touched it. Lacking physical touch, induction is the movement of electrons within a substance as a result of a nearby charged item.
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A horizontal force acts on an object on a fric- tionless horizontal surface. If the force is halved and the mass of the object is doubled, the acceleration will be (1) four times, (2) two times, (3) one-half, (4) one-fourth as great. (b) If the acceleration of the object is , and the force on it is doubled and its mass is halved, what is the new acceleration
(a) If the force is halved and the mass of the object is doubled, the acceleration will be one-fourth as great.
(b) if the force on it is doubled and its mass is halved, the new acceleration will be four times as great.
The force on an object is determined by applying Newton's second law of motion;
F = ma
[tex]\frac{F_1}{m_1a_1} = \frac{F_2}{m_2a_2}[/tex]
(a)
when the force is halved, F₂ = 0.5F₁,
mass is doubled, m₂ = 2m₁
[tex]\frac{F_1}{m_1a_1} = \frac{0.5F_1}{2m_1a_2} \\\\2m_1a_2F_1 = 0.5F_1 m_1a_1\\\\2a_2 = 0.5a_1\\\\a_2 = \frac{0.5a_1}{2} = \frac{a_1}{2 \times 2} = \frac{a_1}{4} \\\\a_2 = \frac{1}{4} (a_1)[/tex]
Thus, If the force is halved and the mass of the object is doubled, the acceleration will be one-fourth as great.
(b)
when the force is doubled, F₂ = 2F₁,
mass is halved, m₂ = 0.5m₁
[tex]\frac{F_1}{m_1 a_1} = \frac{2F_1}{0.5m_1 a_2} \\\\0.5m_1a_2 F_1 = 2F_1m_1a_1\\\\0.5a_2 = 2a_1\\\\a_2 = \frac{2a_1}{0.5} \\\\a_2 = 4(a_1)[/tex]
Thus, if the force on it is doubled and its mass is halved, the new acceleration will be four times as great.
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Explain why adding ice to a drink can cause water droplets (condensation) to appear on the outside of the glass?
Answer:
it just condensed you know it isn't a big deal whatever happens does change anything
l am so confused is it right?
Answer:
D
Explanation:
First,mg＞fv: It does a download acceleration,and the speed of the object increase.
Second,mg=fv: it hasn't a acceleration.
you can think the f is a constant.
9- Where did Rutherford propose that most of the mass of an atom
resided?
a) In the middle of the atom
b) Along the edge of the atom
c) Scattered throughout the atom
d) Orbiting around the atom
Answer:
A) in the middle of the atom
Explanation:
He concluded that all of the positive charge and the majority of the mass of the atom must be concentrated in a very small space in the atom's interior, which he called the nucleus.
which contains the particles that are vibrating fastest?
Answer:
Boiling water
Explanation:
Why does the force between the locomotive and the first car always have to be larger
than the force between the first car and the second?
Answer:
Because the locomotive does most of the pulling
I WILL MARK U HELP PLZ
The free body diagram for an object is projected. Calculate the net force acting on the object. If this object is 10 kg, how/where will it accelerate?
Explanation:
By the end of the section, you will be able to:
Apply problem-solving techniques to solve for quantities in more complex systems of forces
Use concepts from kinematics to solve problems using Newton’s laws of motion
Solve more complex equilibrium problems
Solve more complex acceleration problems
Apply calculus to more advanced dynamics problems
through this steps you will get the answer.thank youA steel projectile is shot horizontally at 54 m/s from the top of a 357 m tower. How far
from the base of the tower does the projectile hit the ground?
Hi there!
We can begin by solving for the time it takes the projectile to reach the ground.
Use the equation:
[tex]t = \sqrt{\frac{2h}{g}}[/tex]
Plug in the given height:
[tex]t = \sqrt{\frac{2(357)}{9.8}} = 8.536 s[/tex]
Use the equation:
d = vt, to solve for the horizontal distance:
d = (54)(8.536) = 460.944 m
whose geocentric model of the solar system was accepted for 1400 years
Answer:
Plato, Aristotle developed it further and used for 1400 years till Copernicus.
Explanation:
what is the acceleration of an object if the force equals 300 N and the mass is 25kg?
Answer:
Explanation: If a net force of 50 N pulls on a 10 kg object, how much acceleration will it cause? Then an answer is possible. Equation: Net force = mass * acceleration.
Explain how solar and lunar eclipse occur with the help of a labelled diagram.
Answer:
a solar eclipse occurs when the moon passes in front of the sun,blocking it out partially or completely. the eclipse results in parts of the earth being covered in the shadow of the moon. a lunar eclipse occurs when the moon passes directly behind earth and into its shadow.
Explanation:
A 1.35 kg block is pulled across a
flat, frictionless floor with a 3.07 N
force at 32.0° above horizontal.
What is the acceleration of the block?
Answer:
F=ma
3.07=1.35(a)
3.07/1.35 = a
a=2.27m/s^2
Explanation:
Since the question gives us both the force and mass of the object we can use the f= ma equation and just plug in both the force and mass and just solve for acceleration. I believe the degree listed in the question is just there to throw you off.
the chemical compositions of jupiter and saturn are most similar to those of:
pls answer the question I will make you as brainiest
Answer:
Answer in the drawing. Please mark me brainliest
a spring vibrates 120 times in 2 mins find its frequency and time period
2 minutes is 120 seconds, so if you were finding vibrations per minute, it would be 60 times a minute.
to analyze the characteristics and performance of the brakes on a 1500 kg car, researchers collected the data shown in the table above. it shows the car’s speed when the brakes are first applied and the corresponding braking distance required to stop the car. the magnitude of the average braking force on the car is most nearly:
He magnitude of the average braking force is 12,000 N.
The braking force can be calculated using the following formula:
Braking Force = (0.5 x mass of the car x squared velocity) / distanceNow, let's use this formula to find the Braking force in each case based on the information of the chart:
F = (0.5 x 1,500 x 100) / 6.1 = 12,295F = (0.5 x 1,500 x 400) / 23.9 = 12,550F = (0.5 x 1,500 x 900) / 53.5 = 12,616Now, let's add the results and divide the result into three to find the average:
12,295 + 12,550 + 12,616 = 37,461/ 3 = 12,487From these, the option that is the most similar is C 12,000 N
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part 3 of 3
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What is the velocity when t = 8 s?
Answer in units of m/s.
Answer in units of m/s
Answer:
1 m/s
(i think, *nervous sweat*)
Explanation:
We can tell this by looking at the graph. When t = 8, we will look at the time. We see that when the x (time) is 8, the velocity is 1 m/s.
what is the acceleration caused by gravity on earth
Answer:
Explanation:
It's 9.8 m/s^2