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°.
To know more about magnitude
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An object has a gravitational force of 111N acting on it. If it had 4 times more mass, what would the force on it be?
Answer:
What is the gravity equation? — It is equal to 6.674×10-11 N·m²/kg². Did you notice that this equation is similar to the formula in Coulomb's law?
Explanation:
A truck brakes from 15 m/s to 2 m/s in 15 seconds. What is its acceleration?
What row of the periodic table does this element belong?
no
14
17
O
18
15
1
16
2.
0 3
Answer:
Group 18
Explanation:
This element has a full octet, therefore it is a noble gas, being in period 18. (I think its Argon if you need that too)
Hope that helps
A ball Of Mass. 0.5 kg initially at rest is kick directly toward offense from appoint 20 m away as shown below the velocity of the ball as it leaves the kickers foot is 16 M/S at angle 45 degrees above the horizontal the top of the fence is 4 m high the ball hits nothing Wallen flight and a resistance is negligible the acceleration due to gravity is 9.8 M/S^2 determine the time it takes for the ball to reach the plane of the fence.
Answer:
a. The horizontal component of the velocity is constant so vxt = d where vx = v0 cosθ = 16m/s t = d/v = 2s
b. The height of the ball during its flight is given by y = v0yt + ½ gt2 where v0y = v0sinθ = 12m/s and g = –9.8m/s2 which gives at t = 2s, y = 4.4m. The fence is 2.5m high so the ball passes above the fence by 4.4m – 2.5m = 1.9m
Explanation:
a boy steps off the end of a high diving board and drops into the water below. it takes the boy 0.78 seconds to reach the water. How high was the diving board?
Answer:
7.644 feet
Explanation:
Free fall means that an object is falling freely with no forces acting upon it except gravity, a defined constant, g = -9.8 m/s2. The distance the object falls, or height, h, is 1/2 gravity x the square of the time falling.
Why do some substances dissolve in water, but other substances do not?
Answer:
It has to do with the polairity of said molelule. If you have vegetable oil, for example, it will not disolve in water because the oil is a non-polar compound, unlike water which is polar. The bond dipoles and differences in electronegetivity in the molecule results in this.
A box is pushed by a force of 15 N and accelerates 2 m/s2. What is the mass of the box?
Answer:
7.5 kgExplanation:
The mass of the box can be found by using the formula
[tex]m = \frac{f}{a} \\ [/tex]
f is the force
a is the acceleration
From the question we have
[tex]m = \frac{15}{2} = 7.5 \\ [/tex]
We have the final answer as
7.5 kgHope this helps you
Zeb was moving his dresser. He pushed with 1000N and the resulting acceleration was 200m/s2. What was its mass?
Answer:
5
Explanation:
Formula for Mass (for this question)
[tex]mass=\frac{Force}{Acceleration}[/tex]
mass= 1000N/200[tex]m^{2}[/tex]=5
(pls do correct me if I have any mistakes it would rlly help others!)
Identify some sports or activities you can do to improve your overall health and explain how physical activity can improve your
Answer:
(Your question isn't finished so here is the full question: Identify some sports or activities you can do to improve your overall health and explain how physical activity can improve your physical and emotional health.)
Answer:
Some sports or activities I can do to improve my overall health are running, jump squats, weightlifting, dancing, yoga and helping out my father in the backyard. Physical activity can improve my physical and emotional health are by strengthening bones/building muscles, control overweight and obesity, reducing stress, and improve my mood.
Explanation:
Hope this helps :)
why do the lights in your home come on almost instantaneously when you turn on the switch?
Answer:
here you go
Explanation:
Why do your lights actually come on almost instantaneously? ... Wiring the house in parallel does not make a difference – there is no current flowing through the light bulb when the switch is off no matter how the house is wired. If there were a current already, the light would be on!
in 10 seconds a car accelerates 4m/s^2 to 50
m/s. How fast was the car going before it accelerated?
Variables:
Equation and Solve:
Answer:
10m/s
Explanation:
using the formula a=v-u
t
Using your knowledge of momentum explain why cars are designed to have crumple zones?
Answer: I think cars are designed to have crumble zone because lets say you're going 60-70 mph and you hit a brick wall that cant move, it would be a very hard jolt causing the beings inside to get thrown forward, but if it has a crumble zone it would slow the the jolt from is slowing down in the hit.
45 KG object has a momentum of 225 KG•m/s northward what is the objects velocity
Answer:
The answer is 5.0 m/s
Explanation:
(Hope this helps can I pls have brainlist (crown)☺️)
WHAT IS PHOTOSYNTHESIS
Answer:
PROCESS BY PLANTS MAKE THIER OWN FOOD WITH THE HELP OF WATER, MINERAL CHLOROPHYLL, CARBON DIOXIDE IN THE PRESENCE OF SUNLIGHT....
I HOPE IT IS HELPFUL
The Sun being the largest body has the highest gravitational pull on all planets however planets do not collapse into the sun this is because of A.gravitational I'll of the Earth B. gravitational pull among the planets C. gravitational pull of Moon D. the balancing force
Answer:
A:gravitational of the earth
As shown above an adhesive has been applied to contacting faces of two blocks so that the blocks interact with an adhesive force that has a magnitude, Fadhesion A tension, T, is exerted by a wire attached to the upper blocks causing the blocks to remain at rest The two blocks have weights, Wbottom and Wtop. Which of the following must be true? (1 point) ♡ O Wtop=T OT = Wtop - Fadhesion O Wbottom Fadhesion O T = Wbottom + Wtop + Fadhesion
The magnitude of the adhesive force allows the top block to remain
attached to the bottom when the blocks and the wire are balanced.
The option that must be true is; [tex]\mathbf{W_{bottom} = F_{adhesion}}[/tex]
Reason:
The tension exerted by the wire attached to the top block = T
Magnitude of the adhesive = [tex]F_{adhesion}[/tex]
Weight of the top block = [tex]W_{top}[/tex]
Weight of the bottom block = [tex]W_{bottom}[/tex]
Given that with the exertion of the tension, the two blocks remain at rest, we have;
T = [tex]W_{top}[/tex] + [tex]W_{bottom}[/tex]The adhesive causes the bottom block to remain attached to the top block, we have;
Therefore, the magnitude of the adhesive force adds the bottom weight, to the top, weight, which gives;
The magnitude of the adhesive force = The weight of the bottom block
Therefore;
[tex]W_{bottom}[/tex] = [tex]F_{adhesion}[/tex]Learn more here:
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Answer:
Wbottom=Fadhersion it was right on y test
Explanation:
calculate the surface area of a circle with radius 3.5 CM
........loke above in the picture
Why are some fibers spun together to form yarns?
Answer:
Spun yarns are produced by placing a series of individual fibres or filaments together to form a continuous assembly of overlapping fibres, usually bound together by twist. This operation is required in wool spinning because different parts of the fleece contain fibres of different length and thickness.
identify the types of elements in the schematic diagram give the number of each types
Where's the diagaram?
how can you reduce the percentage uncertainty in measurements that you make?
Answer:
For example, one method for estimating the length of time it takes something to occur is to time it once using a stopwatch. You can reduce the uncertainty in this estimate by repeating the measurement and taking the average.
There are a lot of way to reduce the uncertainty however with real life sciences like quantum mechanics it will reveal more about the world and life if we have better measuring tools. Being precise is essential to understanding many parts of life.
Hope this helped! Have a great day!!!
what is the term for the matter through which a mechanical wave travels?
Deserts are only found near the equator.
Answer:
False
Explanation:
Texas is and astralia exsist.
what is the energy of light for a single photon that has a wavelength of 347 nm?
The energy of light for a single photon that has a wavelength of 347 nm is 5.698 × 10-¹⁹ J
HOW TO CALCULATE ENERGY:
The energy of a photon of light can be calculated by using the following formula:E = hf
Where;
E = energy of photon (J)h = Planck's constant (6.626 × 10-³⁴J/s)f = frequency (Hz)However, the frequency must first be calculated using the formula as follows:λ = v/f
Where;
λ = wavelengthv = speed of light (3 × 10⁸m/s)f = frequencyf = v ÷ λf = 3 × 10⁸ ÷ 347 × 10-⁹f = 3/347 × 10⁸+⁹f = 0.0086 × 10¹⁷ Hzf = 8.6 × 10¹⁴ HzE = 6.626 × 10-³⁴ × 8.6 × 10¹⁴E = 56.98 × 10-²⁰E = 5.698 × 10-¹⁹ JTherefore, the energy of light for a single photon that has a wavelength of 347 nm is 5.698 × 10-¹⁹ J.Learn more at: https://brainly.com/question/13407202?referrer=searchResults
Una vasca da bagno contiene 1,2 metri cubi di acqua a 35 gradi .Quanti kilogrammi di acqua contiene?
Answer:
te quieroooooooooo❤❤❤❤❤❤❤❤❤❤❤
An object is travelling at a velocity of 5m/s to the right for 5 seconds. If NO forces are applied to the object, what will the velocity of the object be after 5 seconds.
Answer:
Below
Explanation:
We can use this formula to find the final velocity of the object :
vf = vi + at
Now, because no force is applied to the object, the acceleration of this object will be 0 according to Newton's 1st law!
vf = 5m/s + (0)(5)
vf = 5 m/s
Hope this helps!
Pendulum mass is 4 kg. Use your equations for gravitational potential energy and kinetic energy to determine these values based on the data given below. Total energy is the sum of gravitational potential energy and kinetic energy. In this problem, round gravity to: g = 10 m/s2.
its should be 2.0 and 4.5 on it
10. A flower pot falls off the balcony 10 m above the street. How long does it take to hit the
ground?
A laser emits a light beam with a wavelength of 630 nm. The jet passes a liquid with a refractive index of 1.3.
What is the wavelength of the light beam in the liquid?
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 ]Two waves travel through ocean, one with wavelength 3 m, one with 6 m. Which one has greater speed?
Answer: 6m
Explanation: 6 is more than 3 and their both being measured by m