Given:
• Mass, m = 78.0 kg
,• Acceleration = 1.25 m/s²
Let's find the normal force.
To find the normal force, apply the formula for Newton's second law:
[tex]\begin{gathered} \Sigma F_y=ma_y \\ \\ F-mg=-ma \end{gathered}[/tex]Where:
m is the mass of the person = 78.0 kg
a is the acceleration = 1.25 m/s²
g is acceleration due to gravity = 9.8 m/s²
F is the normal force
Thus, we have:
[tex]\begin{gathered} F=mg-ma \\ \\ F=m(g-a) \\ \\ F=78(9.8-1.25) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} F=78(8.55) \\ \\ F=666.9\text{ N} \end{gathered}[/tex]The reading on the scale will be in kilograms.
Hence, we have:
[tex]m=\frac{N}{g}=\frac{666.9}{9.8}=68.1\text{ kg}[/tex]Therefore, the reading on the scale will be 68.1 kg or 666.9 N
ANSWER:
666.9 N
Which picture correctly shows the path of the reflected light rays given an object outside the focal point?Select one:a. Ab. Bc. Cd. D
We will have that the graph that describes the scenario is given by graph B.
A neutral cloth and a neutral rod are rubbed together. Electrons are transferred from the cloth to the rod. What is the final charge on the overall cloth-rod system?A. PositiveB. NeutralC. NegativeD. Not enough info
Given that a neutral cloth and a neutral rod are rubbed together and electrons are transferred from the cloth to the rod.
Let's find the final charge on the overall cloth-rod system.
Here, since a neutral cloth and a neural rod are rubbed together, there is a transfer of charges between both materials.
The metal rod is a conductor while the cloth is an insulator.
As both materials are rubbed together, there is a transfer of electrons. This is due to friction on the materials.
Now, we know that electrons are negatively charged.
As electrons transfer, the rod becomes positively charged while the cloth becomes negatively charged.
Since both materials have opposite charges, the final charge on the overall cloth-rod system will be a NEUTRAL charge.
When a system is neutral, it means that the system has an equal amount of positive and negative cha
• ANSWER:
B. Neutral
A toy that Is 0.5 ft long is used to model the actions of an actual car that is 15 ft long. Which ratio shows the relationship between the sizes of the model and the actual car????
The length of the toy is,
[tex]l=0.5\text{ ft}[/tex]The actual length is given as,
[tex]l^{\prime}=15\text{ ft}[/tex]The ratio of these two values is,
[tex]\begin{gathered} \frac{l}{l^{\prime}}=\frac{0.5}{15} \\ \frac{l}{l^{\prime}}=\frac{1}{30} \end{gathered}[/tex]Thus, the model is 1/30 times size of an actual car.
A 0.09 kg beetle climbs vertically a distance of 0.35 m up a wall at a speed of 0.02 m/s. What is the beetle’s power output?
The power output of the beetle of mass 0.09 kg is 0.0176 W.
What is power?Power is the rate at which work is done per seconds
To calculate the power output of the beetle, we use the formula below.
Formula:
P = mgv............. Equation 1Where:
P = Power output of the beetlem = Mass of the beetlev = Velocity of the beetleg = Acceleration due to gravityFrom the question,
Given:
m = 0.09 kgg = 9.8 m/s²v = 0.02 m/sSubstitute these values into equation 1
P = 0.09×9.8×0.02P = 0.0176 W.Hence, the beetle's power output is 0.0176 W.
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Based on the Mohs Hardness Scale, which mineral could be scratched by a penny but not by a fingernail?Question options:A) FluoriteB) TalcC) CalciteD) Gypsum
Given:
Scale number of a penny = 3.5
Scale number of a fingernail = 2.5
Let's determine the mineral from the options which could be scratched by a penny but not a fingernail.
A mineral with a scale number can scratch any material with equal or lower scale number.
Since a penny has a scale number of 3.5, it can scratch any material with a scale number of 3.5 or lower.
Also, since a fingernail could not scratch the material here, this means the scale number if the material must be greater than 2.5.
Thus, the mineral that could be scratched by a penny but not a fingernail must have a scale number equal to or less than 3.5 but greater than 2.5.
Hence, from the MOHS Hardness Scale, the mineral with a scale number between 3.5 and 2.5 is the Calcite with a scale number of 3.
Therefore, the mineral which could be scratched by a penny but not a fingernail is Calcite.
• ANSWER:
C) Calcite.
Light from red, green and blue spotlights shine on asheet of paper. The paper contains cyan pigment. Whichof the three primary light colors will be absorbed by thepigment?
Given data:
The given colors are red, green, and blue.
The cyan pigment is capable of absorbing red color. The
The correct answer is red light.
Hello could you please help me with this problem? Write an equation in standard form for the line that has an undefined slope and passes through (5,-3).
Answer:
[tex]-3=5m+b[/tex]Explanation: We have to write the equation od line in a standard form that has an unknown slope and passes through (5,-3), in general, the equation of a line is as follows:'
[tex]\begin{gathered} y(x)=mx+b\Rightarrow(1) \\ m=\frac{\Delta y}{\Delta x} \\ b\rightarrow\text{ y-intercept} \end{gathered}[/tex]Passing through a point implies the following:
[tex](x,y)\Rightarrow(5,-3)[/tex]Plugging the x and y in (1) finally gives the following:
[tex]-3=5m+b[/tex]I think this is true I’m not really sure can you explain it?
Assuming there was gravitational force, an object flying upwards would decelerate due its weight. This would cause the velocity to decrease. In this scenario, the area is free of gravitational forces. The velocity is likely to remain the same. Therefore, the engine must not run at some maximum level in order to maintain the ships velocity. Thus, the answer is False
A typical adult ear has a surface area of 2.61× 10-3 m². The sound intensity during a normal conversation is about 2.65 x 10-6 W/m² at the listener's ear. Assume that the sound strikes the surface of the ear perpendicularly. How much power is intercepted by the ear?
ANSWER:
6.9 x 10^-9 W
STEP-BY-STEP EXPLANATION:
Given:
Area (A) = 2.61× 10^-3 m²
Intensity (I) = 2.65 x 10^-6 W/m²
We can determine the power by the following formula:
[tex]\begin{gathered} P=A\cdot I \\ \\ \text{ We replacing:} \\ \\ P=2.61\cdot10^{-3}\cdot2.65\cdot10^{-6} \\ \\ P=6.9\cdot10^{-9}\text{ W} \end{gathered}[/tex]The power is 6.9 x 10^-9 W
A truck is driving 500 meters/minute. He slows down to a complete stop over 0.25minutes. Calculate his acceleration.
Given
The velocity is v=500 meters/minute
The time taken is t=0.25 minute
To find
The acceleration
Explanation
We know,
The acceleration is the ratio of velocity to time.
Thus,
[tex]\begin{gathered} a=\frac{v}{t} \\ \Rightarrow a=\frac{500}{0.25} \\ \Rightarrow a=2000\text{ m/min}^2 \end{gathered}[/tex]Conclusion
The acceleration is
[tex]2000\text{ m/min}^2[/tex]How many kilocalories must be removed from 920 grams of water at a temperature of zero degrees Celsius to transform it into ice at zero degrees Celsius? A)2760 B)497000 C)73.3
Given:
The mass of the water, m=920 g
The temperature of the water, T=0 °C
To find:
The heat required to be removed to transform water to ice.
Explanation:
The latent heat of the fusion of ice is L=79.7 Cal/g.
The latent heat of fusion is the heat that is needed to be removed from the water to convert it into ice.
The amount of the heat that is needed to be removed is given by,
[tex]Q=mL[/tex]On substituting the known values,
[tex]\begin{gathered} Q=920\times79.7 \\ =73324\text{ Cal} \\ \approx73.3\text{ kCal} \end{gathered}[/tex]Final answer:
The amount of heat that is to be removed to convert the given amount of water into ice is 73.3 kCal.
Therefore the correct answer is option C.
A 12 inch-wide conveyor unloads 5000 bushels of wheat per hour. At this speed, how many bushels per hour will an 18-inch-wide conveyor unload?
12-inch wide conveyor unloads 5000 bushels of wheat per hour. At this same speed, the number of bushels that will be unloaded per hour by an 18-inch wide conveyor can be calculated below
[tex]\begin{gathered} 12\text{ = 5000} \\ 18=\text{?} \\ u\text{nload amount=}\frac{5000\times18}{12}=\frac{90000}{12}=7500\text{ bushels per hour } \end{gathered}[/tex]A ball is sliding from the top to the bottom of a plank without rolling (e.g. imagine the surface is covered in ice, so very slippery). The ball is returned to the top and released again, but this time the ball is rolling (without slipping) down the plank (imagine the ice has melted). Compare the speeds of the ball at the bottom.a.The final speed is the same in both cases.b.The final speed is larger in the second case (with rolling).c.The final speed is larger in the first case (without rolling).d.The final speed is larger in the first case (without rolling) if the the plank is at an angle bigger than 45o and smaller if the angle is less than that.
To find:
Compare the speeds of the ball at the bottom of the plank.
Explanation:
From the law of conservation of energy, the total energy of the system always remains constant. Thus the total energy of the ball at the bottom of the plank must be equal to its total energy at the top of the plank.
When the ball is at the top of the plank, the ball has only potential energy. When the ball slides down to the bottom, this potential energy is converted into translational kinetic energy.
The translational kinetic energy is directly proportional to the square of the velocity of the object. Thus when the translational kinetic energy is high the velocity of the ball will be high.
When the ball rolls down the bottom of the plank, the initial potential energy of the ball is converted into translational and rotational kinetic energy.
The rotational kinetic energy of an object is proportional to the square of the angular velocity of the object.
Thus in the first case, the translational kinetic energy and hence the speed of the ball will be larger compared to that in the second case.
Final answer:
Thus the correct answer is option C.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!!
Answer:
a - high thermal conductivity
Answer:
A. high thermal conductivity
Explanation:
high thermal conductivity means a material has the ability to easily take up heat from their environment, in this case the metal pan is taking in heat from it's environment and therefore the mitt is needed.
hope this helps
What is the result of (3.60 m ✕ 1.50 m)/0.50 m with the proper number of significant figures? answer in: m
We will have the following:
[tex]\frac{3.60m\ast1.50m}{0.50m}=10.8\approx11[/tex]So, the solution with the proper number of significant figures is approximately 11. [2 significant figures]
Can you explain the second law of Kepler? Simple terms please
According to Kepler's second law.
The planets move in an elliptical orbit. An elliptical orbit is non-circular which means its radius is not uniform as Sun is present in one of the foci.
According to Kepler's law
Areal speed is constant. This means that when the planet is near the sun, its speed increases and when it is farther from the sun its speed decreases.
When speed is more, the time taken is less and when the speed is less, the time taken will be more.
Thus, areal speed always remains constant.
A car, initially traveling at 2.0 miles per hour, comes to rest in 8.6 s. What was its acceleration in this time?
Given:
the speed of the car is
[tex]u=2.0\text{ mi/h}[/tex]Time during which it comes to rest
[tex]t=8.6\text{ s}[/tex]Required: acceleration is to be calculated
Explanation:
first, convert the speed from miles per hour to meters per second
in doing so we use a conversion factor
that is given as
[tex]1\text{ mi/h= 0.447 m/s}[/tex]Then the speed is ,
[tex]\begin{gathered} u=2.0\text{ }\times0.447 \\ u=0.894\text{ m/s} \end{gathered}[/tex]now calculate the acceleration,
we know that
[tex]v=u+at[/tex]where v is the final velocity that is zero because finally, the car comes to rest.
plugging all the values in the above relation, we get
[tex]\begin{gathered} 0=0.894\text{ m/s }+a\times8.6\text{ s} \\ a=-\frac{0.894}{8.6} \\ a=-0.10\text{ m/s}^2 \end{gathered}[/tex]negative sign shows that acceleration in the opposite direction
Thus, the acceleration is
[tex]0.10\text{ m/s}^2[/tex]find the drag force on a car traveling at 15 m/s. assume that the cars' cross-sectional area is 3.5 m^2, and that air has a density of 1.2 kg/m^3
The drag force on a car traveling at 15 m/s. assume that the cars' cross-sectional area is 3.5 m^2, and that air has a density of 1.2 kg/m^3 will be 472.5 C(d) Newton
Drag force = 1/2 * density of fluid * [tex](speed)^{2}[/tex] * drag coefficient * cross sectional area
= 1/2 * 1.2 * [tex]15^{2}[/tex] * C (d) * 3.5
= 472.5 C(d) Newton
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5. What is the net force on an object with a friction of 50 N toward the left and an applied force of 80 N towards the right?130 N right130 N left30 N left30 N right
Given,
The frictional force is 50 N towards left.
The applied force is 80 N towards right.
Thus the net force is:
F=80N-50N=30 N toards right.
The answer is 30 N towards right.
Suppose two cars are headed toward each other. One is headed north with a mass of1,415 kg at a velocity of 22.9 m/s. The other is headed south with a mass of 819 kg at avelocity 11 m/s. They collide and stick together.What is their total velocity after the collision in the northern direction?
The initial momentum of the system is,
[tex]p_i=m_1u_1+m_2u_2[/tex]The final momentum of the system is,
[tex]p_f=(m_1+m_2)v[/tex]According to conservation of momentum,
[tex]p_i=p_f[/tex]Plug in the known expressions,
[tex]\begin{gathered} m_1u_1+m_2u_2=(m_1+m_{2_{}})v \\ v=\frac{m_1u_1+m_2u_2}{m_1+m_2} \end{gathered}[/tex]Substitute the known values,
[tex]\begin{gathered} v=\frac{(1415\text{ kg)(22.9 m/s)+(819 kg)(11 m/s)}}{(1415\text{ kg+819 kg)}} \\ =\frac{32403.5\text{ kgm/s+}9009\text{ kgm/s}}{2234\text{ kg}} \\ =\frac{41412.5\text{ kgm/s}}{2234\text{ kg}} \\ \approx18.5\text{ m/s} \end{gathered}[/tex]Therefore, the total velocity after the collision is 18.5 m/s
An atom of carbon-14 isotope has more protons than an atom of carbon-12 isotope. Is this true or false?
Carbon-12 and carbon-14 are isotopes of each other. Isotopes are the elements that contain the same number of protons but a different number of neutrons.
CArbon-12 contains six protons and six neutrons. While carbon-14 contains six protons and eight neutrons.
Thus the given statement is false.
Question 3 of 25Which of the following statements is true of the phases of a given substance?A. The particles of a gas are in a fixed location.B. The particles of liquids have more kinetic energy than the particles of gases.C. Gases have strong intermolecular forces between the atoms or molecules.D. The particles of solids have less kinetic energy than the particles of liquids or gases.
ANSWER
D. The particles of solids have less kinetic energy than the particles of liquids or gases.
EXPLANATION
We want to identify the statement that is true about the phases of a given substance.
A gas is a state of matter that expands freely so as to fill the container which contains it. This implies that gases have no fixed shape or location.
The particles of a liquid are more closely packed than gases, implying that motion is restricted for liquids. Since kinetic energy is dependent on motion, it implies that less motion equals less kinetic energy and so liquids have lesser kinetic energy than gases.
In gases, the intermolecular forces are very weak and can be said to be negligible since the particles move freely.
As stated above, kinetic energy is dependent on motion. This means that the more movement that occurs, the more the kinetic energy. The particles of solids are more closely packed than in liquids and gases. This implies that these particles possess less kinetic energy.
Therefore, the correct option is option D.
A 2-newton force applied to a 2-kilogram object caused it to move in a straight line 2 meters during an interval of 2 seconds. The object gains kinetic energy K during this interval. In which of the following cases will the object gain the same kinetic energy K? A. The same force is applied to a 4-kilogram object for the same time. B. The same force is applied to a 4-kilogram object for the same distance.C. A 4-Newton force is applied to a 4-kilogram object for the same time.D. A 4-Newton force is applied to a 4-kilogram object for the same distance.E. The same force is applied to a 4-kilogram object for 4 seconds.
By the kinetic energy theorem we know that:
[tex]W=\Delta K[/tex]where W is the work done by the force and delta K is the change in kinetic energy.
In the original scenario the work done by the force is:
[tex]W=Fd=(2)(2)=4[/tex]Which means that the object gained 4 J in kinetic energy.
Now we need to determine in which scenario given the work done is the same, from the options we notice that in option B we apply the same force for the same distance, which means that the work will be the same and hence the object will gain the same kinetic energy (note that this does not mean that the final velocity will be the same, just that the object will gain the same amount of kinetic energy). In all the other cases we can't conclude the same.
Therefore, the answer is option B.
What is the index of refraction of a substance if the critical angle for a ray going into Water (n=1.33) is 69.30?1.422.2652.11.24
First, remembering Snell's law, we know that:
[tex]sin(\theta)=\frac{n_{entering}}{n_{leaving}}[/tex]So, we know that n_entering is 1.33, as the ray is entering water, and we have the angle, thus:
[tex]sin(69.30°)=\frac{1.33}{n_{leaving}}[/tex]And therefore:
[tex]n_{leaving}=\frac{1.33}{sin(69.30°)}=1.42[/tex]This week, you completed a simulation in which you tested conductivity of various materials to see if you could complete the circuit and light the bulb. The screenshot above shows you a simple circuit, along with an opening for different objects to be tested. Among the objects provided in the simulation are the following:A dollar billA coinA paper clipAn eraserQuestion to answer:Which two objects listed would act as conductors if clipped into the circuit, and which two objects listed would act as insulators? Please include a sentence to summarize how you'd know if each object is considered a conductor or insulator based on the way the circuit is arranged.hi, can someone help me with this? you don’t have to give me an answer or anything cause i know it’s a lot but maybe tell me the steps on how to find the answer?
We will have the following:
From the options provided we can see that the two objects that could act as conductors in order to complete the circuit are the two metallic objects: the coin and the paper clip; reason being that metals are most of the time much better conductors than other materials.
The two objects then that could potentially act as insulators are the dollar bill and the eraser; reason being in part process of elimination and the fact that paper and the material of the eraser are most of the times bad conductors and present a high resistance value due to the nature of the material.
A 120-turn, 9.604-cm-diameter coil is at rest in a horizontal plane. A uniform magnetic field 12 degrees away from vertical increases from 0.316 T to 5.553 T in 98.254 s. Determine the emf induced in the coil.
Given:
The number of turns is,
[tex]n=120[/tex]The diameter of the coil is
[tex]\begin{gathered} d=9.604\text{ cm} \\ =9.604\times10^{-2}\text{ m} \end{gathered}[/tex]The angle of the magnetic field with the coil is
[tex]\theta=12\degree[/tex]The change in a magnetic field is from
[tex]0.316\text{ T to 5.553 T}[/tex]in
[tex]t=98.254\text{ s}[/tex]To find:
The induced emf
Explanation:
The induced emf in the coil is,
[tex]\xi=-nA\frac{dB}{dt}cos\theta[/tex]Here, the area of the coil is,
[tex]\begin{gathered} A=\pi\frac{d^2}{4} \\ =\pi\times\frac{(9.604\times10^{-2})^2}{4} \\ =7.244\times10^{-3}\text{ m}^2 \end{gathered}[/tex]The induced emf is,
[tex]\begin{gathered} \xi=-120\times7.244\times10^{-3}\times\frac{5.553-0.316}{98.254}cos12\degree \\ =-0.045\text{ V} \end{gathered}[/tex]Hence, the induced emf is 0.045 V.
Explain numericals of electricity chapter of class 10 and also diagrams.What is ammeter?What is voltmeter?potential difference?Ohm's law?Resistance?Electric circuitElectric current
Let's explain the following electrical terms.
• Electric current, can be said to be the flow of electric charge. These charges are through a conductor by moving electrons.
• Ammeter, is an instrument used to measure the amount of electric current in a circuit.
The name ammeter was derived from the unit of electric current (Amperes).
• Voltmeter, can be said to be an instrument used to measure the voltage(potential difference) in a circuit. It measures the electric potential between two points in an electrical circuit. It can also be called voltage meter.
• Electric circuit, can be defined as the conductive path for the flow of electric current.
It allows electric charge carriers to flow continuously.
• Resistance ,can be said to be the property of an electrical conductor which resists the flow of electric current. It is measured in ohms.
• Ohms law, states that the potential difference (V) between two points is directly proportional to the electric current across two points.
It is deonted as: V = I x R
Voltage = Current x Resistance
• Electric potential ,can be said to be the amount of electric potential energy at a point.
A girl ties a rope securely to the windowsill of a tower and climbs down to the base of it. She is with a group of friends and wants them to come down too, but easier. She ties the other end of the rope to a tree 30m down and 60m away horizontally, creating a zipline. The first person down the zip line weighs 80 kg. How quickly does he accelerate, and how long does it take for him to reach the end of the zipline?
Answer:
Acceleration = 4.38 m/s²
Time = 5.54 s
Explanation:
We can represent the situation as follows:
So, first, we need to find the angle θ. Using trigonometric functions, we get:
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \text{tan}\theta=\frac{60}{20} \\ \tan \theta=2 \\ \theta=tan^{-1}(2)=63.43 \end{gathered}[/tex]Then, the net force in the direction of the rope is equal to:
[tex]\begin{gathered} F_{\text{net}}=mg\cos \theta \\ F_{\text{net}}=(80\operatorname{kg})(9.8m/s^2)\cos (63.43) \\ F_{\text{net}}=350.62N \end{gathered}[/tex]By the second law of Newton, this force is equal to mass times acceleration, so we can solve for acceleration as follows:
[tex]\begin{gathered} F_{\text{net}}=ma \\ a=\frac{F_{net}}{m}=\frac{350.62N}{80\operatorname{kg}}=4.38m/s^2 \end{gathered}[/tex]So, the first person accelerates at 4.38 m/s².
Now, we need to find the length of the rope. Using the Pythagorean theorem, we get:
[tex]\begin{gathered} L=\sqrt[]{60^2+30^2} \\ L=\sqrt[]{3600+900} \\ L=\sqrt[]{4500}=67.08\text{ m} \end{gathered}[/tex]Then, using a kinetic equation, we get:
[tex]\begin{gathered} x=v_it+\frac{1}{2}at^2 \\ x=\frac{1}{2}at^2 \\ 2x=at^2 \\ \frac{2x}{a}=t^2 \\ t=\sqrt[]{\frac{2x}{a}} \end{gathered}[/tex]Where x is the distance traveled, vi is the initial velocity, which is 0 m/s, a is the acceleration and t is the time.
Now, we can replace x by the length of the rope 67.08m and a by 4.38 to get:
[tex]t=\sqrt[]{\frac{2(67.08)}{4.38}}=5.54\text{ s}[/tex]So, the first person takes 5.54 s to reach the end of the zipline.
Therefore, the answers are
Acceleration = 4.38 m/s²
Time = 5.54 s
A 5.2 × 105 kg subway train is brought to a stop from a speed of 0.55 m/s in 0.51 m by a large spring bumper at the end of its track. What is the force constant k of the spring in N/m?
Given:
The mass of the subway train is,
[tex]m=5.2\times10^5\text{ kg}[/tex]The initial speed of the train is,
[tex]v=0.55\text{ m/s}[/tex]The distance moved by train is,
[tex]x=0.51\text{ m}[/tex]To find:
the spring constant
Explanation:
The kinetic energy of the train converts into the potential energy of the spring. So we can write,
[tex]\begin{gathered} \frac{1}{2}kx^2=\frac{1}{2}mv^2 \\ k=\frac{mv^2}{x^2} \end{gathered}[/tex]Substituting the values we get,
[tex]\begin{gathered} k=\frac{5.2\times10^5\times0.55^2}{0.51^2} \\ =0.60\times10^6\text{ N/m} \end{gathered}[/tex]Hence, the spring constant is
[tex]0.60\times10^6\text{ N/m}[/tex]A green ball (ball 1) of mass M collides with an orange ball (ball 2) of mass 1.26. the initial speed of the green ball is 5.4 m/s the final speed of the green ball is 2.6 m/s and theta=36.9° A. find the magnitude of the final speed of the orange ball? B. what is the direction of the final speed of the orange ball?
Given data:
The mass of ball 1 is m.
The mass of ball 2 is 1.26m.
The initial speed of ball 1 is u=5.4 m/s.
The final speed of the ball 1 U=2.6 m/s.
The angle at which the ball 1 moves from x-axis is θ=36.9.
Applying the conservation of momentum in x-direction,
[tex]\begin{gathered} mu=mU\cos \theta+(1.26m)V\cos \alpha \\ u=U\cos \theta+(1.26)V\cos \alpha \\ 5.4=2.6\cos 36.9+(1.26)V\cos \alpha \\ V\cos \alpha=2.63\ldots\ldots\text{.}(1) \end{gathered}[/tex]Here, V is the final speed of ball 2, and α is the angle of ball 2 with x-axis after the collision.
Applying the conservation of momentum in y-direction,
[tex]\begin{gathered} 0=mU\sin \theta+(1.26m)V\sin \alpha \\ 0=U\sin \theta+(1.26)V\sin \alpha \\ 0=2.6\sin 36.9+(1.26)V\sin \alpha \\ V\sin \alpha=-1.56\ldots\ldots\text{.}(2) \end{gathered}[/tex]Dividing equation (2) and (1),
[tex]\begin{gathered} \frac{V\sin \alpha}{V\cos \alpha}=\frac{-1.56}{2.63} \\ \tan \alpha=0.593 \\ \alpha=30.6\degree \end{gathered}[/tex]Subsitute the value of α in equation (1),
[tex]\begin{gathered} V\cos \alpha=2.63 \\ V\cos 30.6\degree=2.63 \\ V=3.05\text{ m/s} \end{gathered}[/tex]Thus, the final speed of the ball 2 (orange ball) is 3.05 m/s, and the direction of the orange ball is 30.6⁰.