Ball A with diameter d and ball B with diameter 2d are dropped from the same height. When the two balls have the same speed, the ratio of the drag force on ball A to the drag force on ball B will be F1 : F2 = 1 : 4
When objects travel through fluids (a gas or a liquid), they will undoubtedly encounter resistive forces called drag forces.
The drag force always acts in the opposite direction to fluid flow. If the body’s motion exists in the fluid-like air, it is called aerodynamic drag.
formula to calculate drag force is = F(d) = 1/2 * C * rho*A * [tex]v^{2}[/tex]
C = drag coefficient
A = area of object
rho = density in which object is moving
v = velocity of object
A = area of the object
F1 ( drag force on ball A ) = 1/2 * C * rho * area of ball A * [tex]v^{2}[/tex]
F2 (drag force on ball A ) = 1/2 * C * rho * area of ball B * [tex]v^{2}[/tex]
since , both the balls have same speed and falling in same environment hence , density and speeds are the same , the only difference is in area of both the balls
F1/F2 = area of ball A / area of ball B = 4 * pi * [tex]r1^{2}[/tex] / 4 * pi * [tex]r2^{2}[/tex]
= [tex]r1^{2}[/tex] / [tex]r2^{2}[/tex]
= [tex](\frac{d}{2} )^{2}[/tex]/ [tex](\frac{2d}{2}) ^{2}[/tex]
= 1/4
F1 : F2 = 1 : 4
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A baseball of mass 1.23 kg is thrown at a speed of 65.8 mi/h. What is its kinetic energy?
Given:
The mass of the ball is
[tex]m=1.23\text{ kg}[/tex]The speed of the ball is
[tex]\begin{gathered} v=65.8\text{ mi/h} \\ \end{gathered}[/tex]Required: calculate the kinetic energy of the baseball
Explanation: to calculate the kinetic energy of a body we will use the formula as
[tex]K.E=\frac{1}{2}mv^2[/tex]first, we convert velocity from mi/h into m/s.
we know that
[tex]1\text{ mi=1609.34 m}[/tex]and
[tex]1\text{ h=3600 sec}[/tex]then the velocity is
[tex]\begin{gathered} v=\frac{65.8\times1602.34\text{ m}}{3600\text{ s}} \\ v=29.29\text{ m/s} \end{gathered}[/tex]now plugging all the values in the above formula, we get
[tex]\begin{gathered} K.E=\frac{1}{2}mv^2 \\ K.E=\frac{1}{2}\times1.23\text{ kg}\times(29.29\text{ m/s})^2 \\ K.E=527.61\text{ J} \end{gathered}[/tex]Thus, the kinetic energy of the baseball is
[tex]527.61\text{ J}[/tex]The total mechanical energy of the roller coaster cart below at Point A is 180,000 J. The speed of the cart at Point B is +20 m/s. Assume no energy is lost due to dissipative forces such as friction. A) What is the mass (in kg) of the roller coaster cart? B) What is the potential energy at Point A? C) What is the kinetic energy at Point A?
Mechanical energy (ME) = Potential energy(PE) + kinetic energy (KE)
PE = mgh
m= mass
g= gravity
h= height
KE= 1/2 m v^2
v= speed
Point B
ME = KE + PE
PE = 0 (height = 0 )
KE = 1/2 (m) v^2
180,000 = 1/2 (m) (20)^2
m = 180,000 / (1/2 (20)^2 )
m= 900 kg
Point A.
ME = 180,000 J = PEa + KE a
PEa = m g h = 900 (9.8) (20) = 176,400J
MEa = PEa + KEa
KEa = MEa - PEa = 180,000 - 176,400 J = 3,600 J
A) mass = 900 kg
B) 176,400 J
C) 3,600 J
10. A boy of mass 55kg runs at 12m/s and hops on a 15kg skateboard that was at rest. What is thevelocity of the boy on the skateboard afterwards?
M = mass of the boy = 55kg
V = initial velocity of the boy = 12 m/s
m= mass of stationary skateboard = 15kg
v= velocity os stationary sketeboard= 0 m/s
V' = velocity of the boy on the skateboard after collision
Conservation of momentum:
MV + mv = (M + m) V'
Replacing:
55 kg * 12 m/s + 15 kg *0 = (55 kg+ 15 ) V'
Solve for V´'
660 = 70 V´'
660/70 = V'
V'= 9.42 m/s
Convert the following number from scientific notation to standard notation1.9300 x 10^-30.000 193 000.001 93000.001931930
The number converted to the standard notation as
[tex]1.93\times10^{-3}=0.00193[/tex]Hence, the correct answer is 0.00193
Mr.D soars over a large group of zombies and is in the air for a total of 5s. How high did he go?
I need help with this question.The answer choices for each one is eitherAB C D E Any type of help will be appreciated even if it’s just a hint!
Conductor that carries electrons:
From the pic we can conclude that the conductor is the wire, in this case it would be A.
Load that transforms energy:
From the pic, it is the bulb which transform the electric energy into light and heat, so it would be B
Insulation that prevents electrons from flowing:
It is the cable sheath, from the pic it is C
Area of low potential energy for electrons:
It is the negative part of the battery, from the pic it is E
Area of high potential energy for electrons:
It is the positive part of the battery, it is D
What is the energy of a proton accelerated through a potential difference of 500,000 V?
ANSWER
[tex]8.01\cdot10^{-14}J[/tex]EXPLANATION
We want to find the energy of the proton accelerated through the given potential.
To do this, apply the relationship between energy and potential:
[tex]V=\frac{E}{q}[/tex]where q = charge
V = potential
The charge of a proton is:
[tex]1.602\cdot10^{-19}C[/tex]Therefore, we have that the energy of the proton is:
[tex]\begin{gathered} E=V\cdot q \\ E=500000\cdot1.602\cdot10^{-19} \\ E=8.01\cdot10^{-14}J \end{gathered}[/tex]That is the answer.
The chart shows data for four moving objects.
Object
W
X
Y
Z
Which object has the greatest acceleration?
W
Initial Velocity
(m/s)
Ο Ζ
11
10
12
20
Final Velocity
(m/s)
29
34
40
28
Change in
Time (s)
6
12
7
8
Object Y has the greatest acceleration = 4m/s2
What is an acceleration ?
acceleration: the rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. Both effects contribute to the acceleration for all other motions.
Acceleration = (final velocity - initial velocity ) /time
For object W
Acceleration = ( 29-11)/6 = 3m/s2
For object X
Acceleration = (34-10)/12 = 2m/s2
For object Y
Acceleration = ( 40-12)/7 = 4m/s2
For object Z
Acceleration = (28-20)/8 = 1m/s2
Object Y has the greatest acceleration = 4m/s2
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The nearest star to the Earth (other than the Sun) is about 4.0 lightyears away. A lightyear, ly, is the distance light travels in one year. Voyager 1 is traveling at 38,500 miles per hour. How long will it take Voyager 1 to reach the nearest star in years?
First, let's convert the distance of 4 lightyears to miles:
[tex]4\text{ ly}=4\cdot5.879\cdot10^{12}\text{ miles}=23.516\cdot10^{12}\text{ miles}[/tex]Now, let's find the time required:
[tex]\begin{gathered} distance=speed\cdot time\\ \\ 23.516\cdot10^{12}=38500\cdot t\\ \\ t=\frac{23.516\cdot10^{12}}{38500}\\ \\ t=6.10805\cdot10^8\text{ hours} \end{gathered}[/tex]Then, we need to convert from hours to years:
[tex]6.10805\cdot10^8\text{ hours}=\frac{6.10805\cdot10^8}{8760}=6.97266\cdot10^4\text{ years}[/tex]Therefore it will take approximately 69727 years.
17. A material that makes energy transfer difficult is one that is a good...Select one:a. radiator.b. insulator.c. conductor.d. convector.
b. insulator.
The others describe a type of transfer of energy
What laboratory equipment is used to carry or grip a test tube after it has been heated or cooled?
Test tube holder
Explanations:When a test tube is hot or need to be properly held to avoid the spillage of its contents, a test tube holder is the laboratory equipment that is used to grip or hold the test tube.
Therefore, the test tube holder is used for holding or gripping a test tube after it has been heated or cooled
According to Wikipedia, as of November 1, 2021, 4,864 extrasolar planets have been identified. One of the closest multiple-planet solar systems to our own is around the star Gliese 876, about 15 light-years away, and it contains four planets. One takes 63.8 Earth days to revolve, at a distance of 3.07 x 107 kilometers from Gliese 876. Another planet takes 130 Earth days to revolve. How far is this second planet from Gliese 876?
Using kepler's law:
[tex]\frac{T1^2}{r1^2}=\frac{T2^2}{r2^2}[/tex]Where:
T1 = Planet's period of the first planet
T2 = Planet's period of the second planet
r1 = Average distance to Gliese of the first planet
r2 = Average distance to Gliese of the second planet
First, we need to do a conversion:
[tex]\begin{gathered} T1=63.8days\times\frac{24h}{1day}\times\frac{60min}{1h}\times\frac{60s}{1min}=5512320s \\ T2=130days\frac{24h}{1day}\times\frac{60m\imaginaryI n}{1h}\times\frac{60s}{1m\imaginaryI n}=11232000s \end{gathered}[/tex]Now, solving for r2:
[tex]\begin{gathered} r2=\sqrt{\frac{r1^2\cdot T2^2}{T1^2}} \\ r2=\sqrt{\frac{(3.07\times10^7)^2(11232000)^2}{(5512320)^2}} \\ r2\approx62554858.93km \end{gathered}[/tex]Answer:
62554858.93 km
7. Which of the following measurement tools would you need to
determine the temperature of boiling water?
Answer:Laboratory thermometer
Explanation:
A car is going at a speed of 25m/s when the driver puts her foot on the gas pedal. The carfeels a net force of 2000N for 50m. The car's mass is 1000kg.How much kinetic energy does the car have initially?
The initial kinetic energy of the car = 312.5 kJ
Explanation:The initial volume of the car, v = 25 m/s
The mass of the car, m = 1000 kg
The initial kinetic energy is given by the formula
[tex]\begin{gathered} KE=\frac{1}{2}mv^2 \\ \end{gathered}[/tex]Substitute m = 1000 kg, and v = 25 m/s into the formula
[tex]\begin{gathered} KE=\frac{1}{2}\times1000\times25^2 \\ KE=500\times625 \\ KE=312500J \\ KE=312.5kJ \end{gathered}[/tex]The initial kinetic energy of the car = 312.5 kJ
Question 24 of 25What disadvantage of analog signals is overcome by sending digital signals?A. The waves used to transmit analog signals carry more energy.B. The waves used to transmit analog signals are more dangerous.dC. Noise decreases the quality of analog signals.O0D. Noise decreases the loudness of analog signals.SUBMIT
The correct answer is option C, "Noise decreases the quality of the analog signals."
The anlog signals q
The amount of work done by two boys who apply 300 N of force in an unsuccessful attempt to move a stalled car is:1. 600 N · m.2. 300 N.3. 300 N · m.4. 600 N.5. 0.
The work done by a force can be calculated with the formula below:
[tex]W=F\cdot d[/tex]Where W is the work in J, F is the force in N and d is the distance in meters.
Since in this case, the attempt was unsuccessful, the car didn't move, so the distance is zero.
Therefore the work is zero, and the correct option is 5 (work is zero).
According to the law of conservation of charge which statement can be true?A. A silk cloth gained charge. B. A metal rod lost charge.C. A peice of glass transferred electrons to felt. D. A balloon remains neutrally charged when rubbed.
Option D
Explanation:The law of conservation of charge states that the amount of charge in a system is constant
This means that as time changes, the amount of charge in a system does not change
By careful consideration of the options stated:
Each of options A to C either shows that charge is lost or gained
Only option D typifies the law of conservation of conservation of charges because charges are not lost or gained by the ballon so described.
Kathleen is rowing her canoe northward with an average force of 19.1 N. The wind is blowing directly south with an average force of 14.4 N. What is the net force on the canoe?
4.7 N north
33.5 N south
33.5 N north
4.7 N south
The net force on the canoe rowed northward with an average force of 19.1 N is 4.7 N North if the wind is blowing directly south with an average force of 14.4 N.
Net force = Force due to rowing - Force due to wind
Net force = 19.1 - 14.4
Net force = 4.7 N
The direction is towards North because the force due to rowing is greater than the force due to wind.
If two force act in opposite directions, the resultant force is the difference of these two forces and the resultant direction is the direction in which the greater force is applied.
Therefore, the net force on the canoe is 4.7 N North
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What is the kinetic energy of a 2.0 kg object moving at 5 m/s?
Let's put the given values into the formula below and get the result;
[tex]K.E=\frac{1}{2}mv^2[/tex]We know the numerical value of speed. We also know the mass. We can jump straight to the conclusion.
[tex]K.E=\frac{1}{2}(2kg)(5m/s)^2[/tex][tex]=\frac{1}{2}(2kg)(25m^2/s^2)[/tex][tex]=25m^2/s^2=25J[/tex]The Kinetic Energy is 25J.
If we want to accelerate an object, we must apply force on it, after applying Force some work has to be done in which energy should be transferred to the object. The energy is known as kinetic energy. The kinetic energy always depends on the mass and the velocity. It is denoted as K and the Si unit is Joules (J).
To calculate the Kinetic Energy,
K= 1/2 mv^2
m = mass
v = velocity
K = kinetic energy
In solving the above equation,
K = 1/2 x2 x 5^2
K = 5x5
K = 25
The Kinetic Energy is 25J.
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The wave shown below is headed towards the end to the right. What will happen to the wave when it reaches the end of the string?-The wave will be absorbed by the support.-The wave will be reflected but inverted.-The wave will stop at the end of the string. -The wave will be reflected but not inverted.
Answer:
-The wave will be reflected but inverted
Explanation:
This is a transverse wave because the wave is moving to the right and the particles are moving up and down. When a transverse wave reaches the end, it is reflected and inverted so the crest becomes through and the through becomes valleys. So, the answer is
-The wave will be reflected but inverted.
Because when a wave finds a fixed end, the wave is reflected, which means that there will be a wave with the same speed and amplitude but in the opposite direction.
what happens to the state of a variable if it goes through a two series connected NOT gate.
For a convex lens to form a virtual image the object must be located at some distance less than the focal length. Is this true or false?
For a convex lens to form a virtua
Which of the following statements about air is TRUE?
A. Air is not a source of resistance.
B. Air has mass, but not inertia.
C. Air is not affected by human movement.
D. None of these statements are true.
The true statement among the following is that the air is not affected by human movement. Hence, option C is correct.
What is Air?Air relates to the atmosphere of the planet. Several gases and minute dust particles make up the air. Living organisms breathe and thrive in this pure gas. Its shape and volume are ill-defined. Considering that it is matter, it has mass and weight. Atmospheric pressure is generated by air weight. The space vacuum lacks air.
About 78% of the gas within air is nitrogen, 21% of the gas is oxygen, 0.9% of the gas is argon, 0.04% of the gas is co2, and very little other gas is present.
A typical amount of water vapor is around 1%.
Since respiration requires oxygen, animals must breathe it to survive. The lungs transfer back carbon dioxide back into the atmosphere when breathing, putting oxygen into the body.
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Two equal charges q1=q2= -6uC are on the y-axis at y1=3cm and y2= -3cm. What is the magnitude and direction of the electric field on the x-axis at x=4cm. If a test charge q0=2uC is placed at x =4cm find the force the test charge experiences?
The electric field charges, q₁, and q₂, which are each -6×10⁻⁶ μC, gives:
First part:
The magnitude of the electric field at x = 4 cm is -3.456×10⁷ N/CThe direction of the electric field is towards the origin, along the x-axisSecond part:
The force experienced by the charge is 69.12 NWhat is an electric field?An electric field is the field around a particle that is electrically charged and which exerts a force on charged particles within the field.
The given information are:
The electric charges, q₁ = q₂ = -6 μC
The location of the charge q₁ = y₁ = 3 cm on the y-axis
Location of the charge q₂ = y₂ = -3 cm
First part:
The required location of the point where the electric field magnitude and direction is required is x = 4 cm
The electric field formula is: [tex]\displaystyle{E = \frac{k\cdot q}{r^2}[/tex]
Where:
k = The electrostatic constant ≈ 9 × 10⁹ N·m²/C²
The distances, r, of the charges from the required point are therefore obtained using Pythagorean theorem as follows:
r = √(3² + 4²) = 5
r = 5 cm = 0.05 m
Which gives;
[tex]\displaystyle{E = \frac{9 \times 10^9\times (-6) \times 10^{-6}}{(0.05)^2} = -2.16\times 10^{7}[/tex]
Given that the magnitude of the electric field along the y-axis cancel out, the magnitude of the electric field along the x-axis is found as follows:
[tex]E_x = 2 \times -2.16\times 10^{7}\times \dfrac{4}{5} = -3.456 \times 10^7[/tex]
The magnitude of the electric field at x = 4 is -3.456 × 10⁷ N/C
Second part: The magnitude of the test charge is q₀ = 2 × 10⁻⁶ μC
The force of an electric field, F = E × q
The force experienced by the test charge is therefore:
F = -3.456 × 10⁷ × 2 × 10⁻⁶ = -69.12
The force the test charge experiences is 69.12 N acting towards the origin from the point x = 4 cm.
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wat is the mass of the car that has kinetic energy of 2400J and is moving with a speed of 20 m\s
Given,
The kinetic energy of the car, E=2400 J
The speed of the car, v=20 m/s
Kinetic energy is the energy that is possessed by an object due to its motion.
It is given by,
[tex]E=\frac{1}{2}mv^2[/tex]Where m is the mass of the car.
On substituting the known values in the above equation,
[tex]\begin{gathered} 2400=\frac{1}{2}\times m\times20^2 \\ m=\frac{2\times2400}{20^2} \\ =\frac{4800}{400} \\ =12\text{ kg} \end{gathered}[/tex]Thus the mass of the car is 12 kg
20. A 15.9kg rock is dropped from a height of 113m. Calculate its potential energy. What is the rock'skinetic energy right before it hits the ground? What is the rock's velocity right before it hits the ground?
Kinetic energy = 1/2 * m * v^2
Potential energy = m*g*h
m = 15.9 kg
h= 113 m
Potential energy = 15.9 kg * 9.8 N * 113 m = 17,607.66 J
Kinetic energy right before it hits the ground
PE = KE
mgh = 1/2 m v^2
Masses cancel out
gh = 1/2v^2
9.8 N * 113m = 1/2 v^2
Solve for v
1,107.4 Nm = 1/2 v^2
1,107.4 Nm / (1/2) = v^2
2,214.8 Nm = v^2
√2,214 = v
47.06 m/s = V
Kinetic energy : 1/2 * m * v^2 = 1/2 * 15.9 * 47.06^2 = 17,606.41 J
Projections of a vector make up the components of that vector. Is this true or false?
The given statement 'Projections of a vector make up the components of that vector' is true. The direction of a vector
A 1500 kg car traveling at 10 m/s suddenly runs out of gaswhile approaching the valley shown in FIGURE EX10.11. The alertdriver immediately puts the car in neutral so that it will roll.What will be the car’s speed as it coasts into the gas station onthe other side of the valley?
If the car does not brake, its mechanical energy will be conserved along all its trajectory.
Then, the sum of the kinetic energy (K) of the car and its gravitational potential energy (U) will be the same for any two points in the trajectory:
[tex]K_1+U_1=K_2+U_2[/tex]The kinetic energy of an object with mass m and speed v is:
[tex]K=\frac{1}{2}mv^2[/tex]The gravitational potential energy of an object with mass m at a height h above a reference level, is:
[tex]U=mgh[/tex]Where g is the acceleration of gravity.
In the beginning, the car has a height of 10m and a speed of 10m/s. In the end, the car reaches the gas station at a height 15m and a unknown speed v.
Then, the initial speed and height are known, as well as the final height. Use the equation for the conservation of mechanical energy to isolate v_2, the unknown final speed of the car:
[tex]\begin{gathered} K_2+U_2=K_1+U_1 \\ \Rightarrow\frac{1}{2}mv_2^2+mgh_2=\frac{1}{2}mv_1^2+mgh_1 \\ \Rightarrow\frac{1}{2}v_2^2+gh_2=\frac{1}{2}v_1^2+gh_1 \\ \Rightarrow\frac{1}{2}v_2^2=\frac{1}{2}v_1^2+gh_1-gh_2 \\ \Rightarrow\frac{1}{2}v_2^2=\frac{1}{2}v_1^2+g\mleft(h_1-h_2\mright) \\ \Rightarrow v_2^2=v_1^2+2g\mleft(h_1-h_2\mright) \\ \\ \therefore v_2=\sqrt{v_1^2+2g(h_1-h_2)} \end{gathered}[/tex]Replace v_1=10m/s, h_1=10m, h_2=15m and g=9.8m/s^2 to find the speed of the car as it reaches the gas station:
[tex]\begin{gathered} v_2=\sqrt{(10\frac{m}{s})^2+2(9.8\frac{m}{s^2})(10m-15m)} \\ =1.4142...\frac{m}{s} \\ \approx1.4\frac{m}{s} \end{gathered}[/tex]Therefore, the car's speed as it coasts into the gas station on the other side of the valley will be approximately 1.4 meters per second.
A roller coaster has a vertical loop with radius 22.8 m. With what minimum speed should the roller-coaster car be moving at the top of the loop so that the passengers do not lose contact with the seats?
Given,
The radius of the loop of the roller coaster, r=22.8 m
The forces that are acting on the roller coaster when it is at the top of the loop are the centripetal force directed upwards and the weight of the roller coaster including the passengers directed downwards.
For the passengers to stay in the seat, the centripetal force must be, at the least, equal to the weight of the passengers and the rollercoaster.
That is,
[tex]\frac{Mv^2}{r}=Mg[/tex]Where M is the combined mass of the rollercoaster and the passengers, v is the minimum speed of the roller coaster when it is at the top of the loop, and g is the acceleration due to gravity.
On simplifying the above equation,
[tex]v=\sqrt[]{gr}[/tex]On substituting the known values,
[tex]\begin{gathered} v=\sqrt[]{9.8\times22.8} \\ =14.95\text{ m/s} \end{gathered}[/tex]Thus the minimum speed that the roller coaster must have when it is at the top of the loop so that the passengers stay in contact with the seats is 14.95 m/s.
Find the direction of the vector A⃗ = (5.1 m )x^ + (-1.5 m )y^.Find the direction of the vector B⃗ = (-1.5 m )x^ + (5.5 m )y^Find the magnitude of the vector A⃗ +B⃗ .Find the direction of the vector A⃗ +B⃗ .
The angle between the components x and y of a vector is given by:
[tex]\theta=\tan ^{-1}(\frac{v_x_{}_{}}{v_y})[/tex]once we know this we need to find in which quadrant the vector lies so we know how to calculate the correct direction.
Vector A lies in the fourth quadrant this means that we need to subtract theta to 360° in order to get the direction of the vector, then we have:
[tex]360-\tan ^{-1}(\frac{1.5}{5.1})=343.61[/tex]Therefore the direction of vector A is 343.61°
Vector B lies in the second quadrant, this means that we need to subtract theta (given by the first equation) to 180° in order to get the direction, then we have:
[tex]180-\tan ^{-1}(\frac{5.5}{1.5})=105.26[/tex]Therefore the direction of vector B is 105.26°
Let's find vector A+B:
[tex]\begin{gathered} \vec{A}+\vec{B}=\langle5.1,-1.5\rangle+\langle-1.5,5.5\rangle \\ =\langle5.1-1.5,-1.5+5.5\rangle \\ =\langle3.6,4\rangle \end{gathered}[/tex]Then we have that:
[tex]\vec{A}+\vec{B}=\langle3.6,4\rangle[/tex]To find its magnitude we have to remember that the magnitude of any vector is given by:
[tex]\lvert\vec{v}\rvert=\sqrt[]{v^2_x+v^2_y}[/tex]Then for vector A+B we have:
[tex]\begin{gathered} \lvert\vec{A}+\vec{B}\rvert=\sqrt[]{(3.6)^2+(4)^2} \\ =5.38 \end{gathered}[/tex]Therefore the magnitude of vector A+B is 5.38 meters.
Vector A+B lies in the first quadrant, then its direction is given by the expression for theta, then we have:
[tex]\tan ^{-1}(\frac{4}{3.6})=48.01[/tex]Therefore the direction of vector A+B is 48.01°