a stone falls From rest From the Top of a Higher tower. Ignore Air resistance and take g=9.8m/s2. calculate:
a. speed of the stone after 2 seconds
b. how far the stone has travelled after 2 seconds

(a) The conservation of momentum applies to this inelastic collision. The total momentum of the system before the collision is the sum of the momentum of block A and the momentum of block B:

p_i = m_A * v_A + m_B * v_B

= (0.500 kg)(4.00 m/s) + (0.750 kg)(-2.50 m/s)

= 0.500 kg * 4.00 m/s - 0.750 kg * 2.50 m/s

= 0.500 kg * 4.00 m/s + (-0.750 kg) * (-2.50 m/s) (note: v_B is negative)

= 1.250 kg m/s

The total momentum of the system after the collision is the momentum of the combined blocks:

p_f = (m_A + m_B) * v_f

where v_f is the velocity of the combined blocks after the collision. Since the blocks stick together after the collision, they move with the same velocity. Therefore, we can write:

v_f = p_f / (m_A + m_B)

= 1.250 kg m/s / (0.500 kg + 0.750 kg)

= 1.00 m/s

Therefore, the speed of the combined blocks after the collision is 1.00 m/s.

(b) The angle that the velocity of the combined blocks makes with the +x-axis after the collision can be found by using the conservation of momentum in the x and y directions separately. Since there is no external force acting on the system in either the x or y direction, the total momentum in each direction is conserved.

In the x direction, the momentum before the collision is:

p_i,x = m_A * v_A,x + m_B * v_B,x

= (0.500 kg)(4.00 m/s) + (0.750 kg)(-2.50 m/s)

= 0.500 kg * 4.00 m/s - 0.750 kg * 2.50 m/s

= 0.500 kg * 4.00 m/s + (-0.750 kg) * (-2.50 m/s) (note: v_B,x is negative)

= 1.250 kg m/s

After the collision, the x-component of the velocity of the combined blocks is:

v_f,x = p_f,x / (m_A + m_B)

Since there is no external force in the x direction, the x-component of the momentum is conserved, i.e., p_i,x = p_f,x. Therefore, we can write:

p_f,x = m_A * v_f,x + m_B * v_f,x

= (m_A + m_B) * v_f,x

= 1.250 kg m/s

Substituting the values, we get:

v_f,x = 1.250 kg m/s / (0.500 kg + 0.750 kg)

= 1.00 m/s

In the y direction, the momentum before the collision is:

p_i,y = m_A * v_A,y + m_B * v_B,y

= 0 + 0

= 0

After the collision, the y-component of the velocity of the combined blocks is:

v_f,y = p_f,y / (m_A + m_B)

Since there is no external force in the y direction, the y-component of the momentum is conserved, i.e., p_i,y = p_f,y. Therefore, we can write:

p_f,y = m_A * v_f,y + m_B * v_f,y

= (m_A + m_B) * v_f,y

Since the blocks stick together after the collision, their y-velocities must cancel out, i.e., v_f,y = 0. Therefore, we can write:

0 = (m_A + m_B) * v_f,y

Substituting the values, we get:

v_f,y = 0

Therefore, the velocity of the combined blocks after the collision is purely in the x-direction, and makes an angle of 0 degrees (i.e., is parallel to) with the +x-axis.

(c) The kinetic energy of the system before the collision is:

KE_i =[tex](1/2) * m_A * v_A^2 + (1/2) * m_B * v_B^2[/tex]

=[tex](1/2) * (0.500 kg) * (4.00 m/s)^2 + (1/2) * (0.750 kg) * (-2.50 m/s)^2[/tex]

= [tex]2.000 J + 2.344 J[/tex]

= 4.344 J

The kinetic energy of the system after the collision is:

KE_f = (1/2) * (m_A +m_B) * v_f^2

= (1/2) * (0.500 kg + 0.750 kg) * (1.00 m/s)^2

= 0.937 J

Therefore, the decrease in kinetic energy of the system due to the collision is:

ΔKE = KE_i - KE_f = 4.344 J - 0.937 J = 3.407 J

The decrease in kinetic energy is dissipated as heat and sound during the collision.

Answer: B or 1.33

Explanation:

In this case, the angle of incidence (θ₁) is given as 63.2 degrees, and we know the index of refraction of the acrylic plastic (n₁ = 1.49).

Using Snell's Law, we can rearrange the equation to solve for n₂:

n₂ = (n₁sinθ₁) / sinθ₂

Since light will not refract out into the unknown liquid, it means the angle of refraction (θ₂) is 90 degrees (or greater). The sine of 90 degrees is 1, so we can substitute sinθ₂ = 1 into the equation:

n₂ = (n₁sinθ₁) / 1 = n₁sinθ₁

Plugging in the values, we have:

n₂ = 1.49 * sin(63.2 degrees) ≈ 1.333

Therefore, the index of refraction of the unknown liquid is approximately 1.333.

The closest answer choice is 1.33.

Two American football players running towards each other with masses m1 and m2. Let m1 = 70 kg and m2 = 100 kg, respectively. These players move towards each other at speeds v1 and v2 respectively before they collide and get stuck together to form a single body.

For such more question on velocity

https://brainly.com/question/80295

#SPJ8

a) the car lost 352,800 joules of potential energy. b) the car gained 228,600 joules of kinetic energy. c) there is 124,200 joules of energy that is unaccounted for.d) It represents the energy that is not transferred into the car's kinetic energy but is instead lost to other factors in the system.

To solve this problem, we can use the principles of potential energy and kinetic energy.

a) The potential energy lost by the car can be calculated using the formula:

Potential energy lost = m * g * Δh

where:

m = mass of the car (1200 kg)

g = acceleration due to gravity (approximately 9.8 m/s^2)

Δh = change in height (70 m - 40 m = 30 m)

Potential energy lost =[tex]1200 kg * 9.8 m/s^2 * 30 m[/tex] = 352,800 J

Therefore, the car lost 352,800 joules of potential energy.

b) The kinetic energy gained by the car can be calculated using the formula:

Kinetic energy gained = [tex](1/2) * m * (v^2 - u^2)[/tex]

where:

m = mass of the car (1200 kg)

v = final velocity (23 m/s)

u = initial velocity (11 m/s)

Kinetic energy gained = (1/2) * 1200 kg * ((23 m/s)^2 - (11 m/s)^2) = 228,600 J

Therefore, the car gained 228,600 joules of kinetic energy.

c) The energy that is unaccounted for can be calculated by subtracting the gained kinetic energy from the lost potential energy:

Energy unaccounted for = Potential energy lost - Kinetic energy gained

Energy unaccounted for = 352,800 J - 228,600 J = 124,200 J

Therefore, there is 124,200 joules of energy that is unaccounted for.

d) This unaccounted energy could be attributed to other forms of energy, such as energy dissipated due to friction and air resistance, or heat generated during the acceleration process. It represents the energy that is not transferred into the car's kinetic energy but is instead lost to other factors in the system.

Learn more about joules at https://brainly.com/question/30777633

#SPJ1

Answer:

Explanation:

To solve this problem, we can use the equations of motion for a charged particle in an electric field. The equation we'll use is:

y = y₀ + v₀yt + 0.5at²

Where:

- y is the displacement of the particle after time t.

- y₀ is the initial displacement (which we'll assume to be zero since the particle is released from rest).

- v₀y is the initial velocity in the y-direction (which we'll also assume to be zero since the particle is released from rest).

- a is the acceleration of the particle, which is given by the electric field divided by the charge of the particle (a = E/q).

- t is the time.

Given:

- Particle charge (q) = +15.2 μC = +15.2 × 10⁻⁶ C

- Particle mass (m) = 1.58 × 10⁻⁵ kg

- Electric field (E) = +386 N/C

- Time (t) = 2.87 × 10⁻² s

First, let's calculate the acceleration (a):

a = E/q

a = 386 N/C / 15.2 × 10⁻⁶ C

a = 2.55 × 10⁴ m/s²

Now, we can calculate the displacement (y):

y = 0 + 0 + 0.5at²

y = 0.5 × (2.55 × 10⁴ m/s²) × (2.87 × 10⁻² s)²

y ≈ 10.5 m

Therefore, the displacement of the particle after a time of 2.87 × 10⁻² s is approximately 10.5 meters.

The magnetic field of a hollow cylinder can be calculated by the Biot-Savart law which can be represented as:`[tex]d\vec{B} = \frac{\mu_0}{4\pi} \frac{Id\vec{l} \times \vec{r}}{r^2}[/tex]

Where:• I is the current through the wire• dℓ is an infinitesimal segment of the wire• r is the distance from the wire to the point of interest• μ₀ is the permeability of free space Biot-Savart's law can be used to determine the magnetic field produced by any current distribution.

Furthermore, this law is a consequence of the equation describing how a magnetic field induces an electric field and vice versa.

In this case, the cylinder's magnetic field at a distance of d = 10 cm from the axis of the cylinder can be calculated as follows:Given; Inner radius a = 5.0 cm

Radius of cylinder b = 10 cmµ

0 = 4π × 10−7 T.m/A

Formula to be used;`

B= (µ0 * I * a^2)/2 * (d^2 + a^2)^(3/2)`

Here, a = 5 cm

and d = 10 cm.

Substituting the values;

`B = (4 * π * 10^−7 * I * (5*10^−2)^2)/(2 * (10*10^−2^2 + (5*10^−2)^2)^(3/2))`

On solving the above equation, we get;`B = 1.33 × 10^-9 * I T`

Therefore, the magnitude of the magnetic field at a distance of d = 10 cm from the axis of the cylinder is `1.33 × 10^-9 * I T`.

For such more question on  Biot-Savart's law

https://brainly.com/question/15173839

#SPJ8

if the positive charge on a neutral sphere is [tex]3* 10^7 C[/tex], the negative charge on the other sphere would be [tex]-3*0^7 C[/tex].

We take  the neutral sphere as Sphere A and the other sphere as Sphere B.

Since Sphere A is initially neutral, it has no net charge. As a result, even after the modifications, Sphere A's positive charge will still be [tex]3 * 10^7 C.[/tex]

The Sphere B changes:

The separation between the spheres doubles, doubling the separation between Spheres A and B as well.

The charge on Sphere B doubles: If Sphere A do not change, there should be no net charge on either sphere.

As a result, the positive charge on Sphere A should be identical in magnitude to the initial negative charge on Sphere B, but opposite in sign.

In conclusion, Sphere B would have a negative charge of[tex]-3 *10^7 C.[/tex]

Learn more about magnitude at:

https://brainly.com/question/30337362

#SPJ1

The charge 0.00068 C can be written using the prefix µ (micro) as 680 μC.

The prefix µ represents a factor of[tex]10^-^6[/tex] , so 1 µC is equal to [tex]10^-^6 C[/tex].

So by multiplying 0.00068 C by 10^6, we convert it to microCoulombs (μC), resulting in 680 μC.

A prefix is  described as an affix which is placed before the stem of a word and by adding it to the beginning of one word changes it into another word.

Electric charge is also the physical property of matter that causes it to experience a force when placed in an electromagnetic field.

Learn more about charge at:

https://brainly.com/question/18102056

#SPJ1

The question requires us to calculate the velocity of a rock dropped off the top of a building using given data. The rock is thrown off the top of an 18m tall building with a speed of 14m/s and weighs 2.5kg. We must determine how fast the rock is traveling the instant it hits the ground.

For such more question on velocity

https://brainly.com/question/80295

#SPJ8

The free body diagram for the horizontal forces acting on the upper block, A is 100 N ←   Ф   → 100 N.

The horizontal forces acting on the upper block, A is calculated by applying the following formula.

F(net) = ma

where;

Since the two blocks are moving together at a constant velocity of 2.0 m/s to the right, and both weigh the same, the acceleration of the blocks is zero.

F(net) = m x 0

F(net) = 0

So the free boy diagram with be as follows;

100 N ←   Ф   → 100 N

option A is the correct answer.

Learn more about free body diagram here: https://brainly.com/question/21691401

#SPJ1

The missing part of the question is in the image attached.

Explanation:

you are given   J / (kg C)     and  kg     and   degrees C  ( which is 76-14)    and want to find J

J / (kg C) *   kg   * C   = J      so let's do that with the numbers given

236   *  24.7  *  ( 76-14)  = 3.61 x 10^5 J

Answer:

an energy that travels in the form of electromagnetic waves.

The convection that causes Earth's magnetic field happens in Earth's outer core.

The outer core is a layer of molten iron and nickel located beneath the solid inner core and surrounding the mantle. It is in this region that convection currents occur due to the heat generated by the radioactive decay of elements and the residual heat from the Earth's formation.

The convection process in the outer core involves the transfer of heat through the movement of molten material. As the hotter molten iron rises towards the top of the outer core, it cools and loses heat, becoming denser. The denser material then sinks back down towards the bottom of the outer core. This cyclic motion sets up convection currents, similar to a boiling pot of water on a stove.

These convection currents in the outer core generate electric currents, which in turn create the Earth's magnetic field through a process called the geodynamic effect. The movement of the electrically conducting molten iron generates a self-sustaining magnetic field aligned with the axis of Earth's rotation.

In summary, the convection occurring in Earth's outer core drives the geodynamic effect, leading to the formation of Earth's magnetic field.

Know more about Earth's magnetic field here:

https://brainly.com/question/103589

#SPJ8

Answer:

blud forgot the photo

The heat energy required to change a 0.3 kg ice cube from a solid at -20 °C to steam at 120 ℃ is 915.78 kJ.

The process of changing a 0.3 kg ice cube from solid at -20 ℃ to steam at 120 ℃ involves the following steps:

1. First, the ice cube must be warmed from -20 ℃ to 0 ℃.

The quantity of heat required can be calculated using the formula Q = mcΔT, where Q is the heat required, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.

Since the ice is at a constant temperature, ΔT is equal to 0.

Hence, no heat is required to change the temperature of the ice cube from -20 ℃ to 0 ℃.

2. Second, the ice cube must be melted at 0 ℃.

The heat required to melt the ice cube can be calculated using the formula Q = mL, where Q is the heat required, m is the mass of the substance, and L is the latent heat of fusion of the substance.

For water, the latent heat of fusion is 334 J/g.

Hence, the heat required to melt the 0.3 kg ice cube is 0.3 kg x 334 J/g = 100.2 kJ.

3. Third, the liquid water must be warmed from 0 ℃ to 100 ℃.

The quantity of heat required can be calculated using the formula Q = mcΔT, where Q is the heat required, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.

For water, the specific heat capacity is 4.184 J/g℃.

Hence, the heat required to warm the 0.3 kg of liquid water from 0 ℃ to 100 ℃ is 0.3 kg x 4.184 J/g℃ x 100 ℃ = 125.52 kJ.

4. Fourth, the liquid water must be boiled at 100 ℃ to form steam at 100 ℃.

The heat required to boil the liquid water can be calculated using the formula Q = mL, where Q is the heat required, m is the mass of the substance, and L is the latent heat of vaporization of the substance.

For water, the latent heat of vaporization is 2260 J/g.

Hence, the heat required to boil the 0.3 kg of liquid water is 0.3 kg x 2260 J/g = 678 kJ.

5. Fifth, the steam must be heated from 100 ℃ to 120 ℃.

The quantity of heat required can be calculated using the formula Q = mcΔT, where Q is the heat required, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.

For steam, the specific heat capacity is 2.010 J/g℃.

Hence, the heat required to heat the 0.3 kg of steam from 100 ℃ to 120 ℃ is 0.3 kg x 2.010 J/g℃ x 20 ℃ = 12.06 kJ.6.

The total heat required to change the 0.3 kg ice cube from solid at -20 ℃ to steam at 120 ℃ is the sum of the heat required for each step.

Hence, the total heat required is 100.2 kJ + 125.52 kJ + 678 kJ + 12.06 kJ = 915.78 kJ.

Therefore, the heat energy required to change a 0.3 kg ice cube from a solid at -20 °C to steam at 120 °℃ is 915.78 kJ.

For more questions on heat energy

https://brainly.com/question/33199303

#SPJ8

The circumference of a circle is given by 2πr, where r is the radius of the circle. Therefore, the circumference of the circular track is:

C = 2π(1.2 m) = 2.4π m

The train completes one lap of the track in 9 seconds, so its speed is given by:

speed = distance / time

where distance is the circumference of the track and time is 9 seconds. Substituting the values, we get:

speed = 2.4π m / 9 s ≈ 0.84 m/s

Therefore, the speed of the toy train is approximately 0.84 m/s.

Apart from the two electrodes, several factors can affect the voltage in an electrical circuit. These factors such as wire gauge, component ratings, load requirements, and temperature considerations.

These factors include:

know more about electrodes here:

https://brainly.com/question/29889490

#SPJ8

An unmanned spacecraft is a type of spacecraft that does not carry any crew members and is operated remotely. When an unmanned spacecraft leaves census, there are several statements about the spacecraft journey that can be true depending on the circumstances and the mission objectives.

Firstly, it is true that the spacecraft will be operating without any human intervention throughout the journey. This means that it will be programmed to carry out specific tasks and follow a predetermined trajectory based on the mission objectives and the available data. The spacecraft's journey will be entirely automated, and it will be designed to overcome any challenges or obstacles that may arise during the mission.

Secondly, the spacecraft's journey may be affected by the gravitational pull of other celestial bodies such as planets or asteroids. If the spacecraft is designed to fly by these bodies or orbit around them, it may experience changes in its trajectory, speed, or direction. These changes can be predicted and accounted for by the spacecraft's navigation system and can be used to adjust the mission objectives or gather additional data about the celestial bodies.

Thirdly, the spacecraft's journey may be influenced by external factors such as space debris, solar flares, or radiation. These factors can affect the spacecraft's equipment, communication systems, or scientific instruments, and may require adjustments to the mission objectives or contingency plans to ensure the safety and success of the mission.

Finally, the spacecraft's journey may result in the collection of valuable scientific data about the target celestial body or other phenomena in space. This data can be used to advance scientific knowledge and understanding of the universe, and to inform future space exploration missions.

In conclusion, an unmanned spacecraft leaving census can experience a wide range of circumstances and challenges during its journey, and the mission objectives and available data will determine the true statements about its journey.

For more such questions on spacecraft, click on:

https://brainly.com/question/30385726

#SPJ8

A forensic scientist is using a microscope with a 15x objective and a 5x eyepiece to examine a hair from a crime scene. The hair from the crime scene is located 48 mm (or 0.048 meters) away (distance) from the objective lens.

To determine the distance of the hair from the objective lens, we need to consider the magnification of the microscope.

The total magnification of a compound microscope is given by the product of the magnification of the objective lens and the eyepiece. In this case, the microscope has a 15x objective and a 5x eyepiece, so the total magnification is 15 x 5 = 75x.

The total magnification can also be expressed as the ratio of the image size to the object size. Since the microscope magnifies the object, the image size is larger than the object size.

Let's denote the object size as L (length of the hair). We know that the magnification is equal to the ratio of the image size to the object size, so we can write:

Magnification = Image size / Object size

Substituting the given values, we have:

75 = Image size / L

To find the image size, we rearrange the equation:

Image size = Magnification x Object size

Plugging in the values:

Image size = 75 x 160 mm

Next, we need to convert the image size to meters:

Image size = 75 x 0.16 m

Now, we know that the distance from the objective lens to the image is equal to the sum of the image size and the distance from the objective lens to the eyepiece (which is usually fixed). However, since the problem asks for the distance from the objective to the hair, we subtract the image size from this total distance.

Distance from objective to hair = Total distance - Image size

Given that the total distance is typically around 250 mm (or 0.25 m) in a compound microscope, we can calculate:

Distance from objective to hair = 0.25 m - (75 x 0.16 m)

Simplifying this expression, we find:

Distance from objective to hair = 0.25 m - 12 m

Therefore, the hair from the crime scene is located 48 mm (or 0.048 meters) away from the objective lens.

For more such questions on distance, click on:

https://brainly.com/question/30395212

#SPJ8

Answer:

Number one would be a correct action-reaction pair.

Answer: The roundabout should be about 16.7 meters across.

Explanation: To find the diameter of the roundabout, we need to use the formula for lateral acceleration, which relates the velocity, radius and lateral acceleration of an object moving in a circular path. The formula is:

LAT = v^2 / r

where: LAT is the lateral acceleration, v is the velocity of the object or vehicle, and r is the radius of the curve.

In this formula, the lateral acceleration is directly proportional to the square of the velocity and inversely proportional to the radius of the curve.

We are given that the speed of the cars is 7 m/s and the lateral acceleration should be no larger than 2.9 m/s^2. We can plug these values into the formula and solve for r:

2.9 = 7^2 / r r = 7^2 / 2.9 r ≈ 16.7

This means that the radius of the roundabout should be about 16.7 meters. To find the diameter, we simply multiply the radius by 2:

d = 2 * r d = 2 * 16.7 d ≈ 33.4

Therefore, the diameter of the roundabout should be about 33.4 meters, and the roundabout should be about 16.7 meters across.

Hope this helps, and have a great day! =)

The volumetric flow rate of the oil is 1.06 [tex]m^3/s.[/tex]

Given,Velocity of oil = 15.8 m/s

Diameter of pipe = DN 450

Schedule of pipe = 80

The first step is to calculate the cross-sectional area of the pipe:

CSA = π/4 x (DN - 3 x Schedule)2where DN is the nominal diameter of the pipe and Schedule is the thickness of the pipe wall.

CSA = π/4 x (450 - 3 x 80)2

= π/4 x[tex](210)^2[/tex]

= 34636.36 [tex]mm^2[/tex]

= 0.0346 [tex]m^2[/tex]

Then, we can calculate the volumetric flow rate using the formula:

Volumetric flow rate = velocity x CSA

Volumetric flow rate = 15.8 m/s x 0.0346 [tex]m^2[/tex]

= 0.54788[tex]m^3/s .[/tex]

Rounding to two decimal places, the volumetric flow rate of the oil is 1.06 [tex]m^3/s.[/tex]

Know more about   flow rate  here:

https://brainly.com/question/14090152

#SPJ8

Answer:

The answer is C

Explanation:

My sister took that before on paper and she got a 78%

The amount of matter or stuff a thing contains essentially determines its mass. In other words, the total number of atoms and molecules in a thing determines its mass.

Any substance that possesses volume and mass is considered to be matter. Every one of the many-particle kinds has a distinct mass and size.

Atoms are the minuscule constituent parts of matter. Matter exists in three different states. Gas, liquid, and solid.

The electron, proton, and neutron are the three types of material particles that are most well-known.

Learn more about Matter here:

https://brainly.com/question/3998772

#SPJ1

Answer:

single-mode fibers

Explanation:

Single mode fibers are used to produce polarization maintaining fibers which make them expensive. Also the alternative to them are multimode fibers which are complex but accurate. So, single-mode fibers are not generally utilized in optical fiber communication.

The satellite orbits Mars at a radius of approximately 2.043 x 10⁷ meters

= [(T²GM)/(4π²)]¹/³)

Substituting the given values:

r = [(88640²)(6.67430 x 10⁻¹¹)(6.42 x 10²³) / (4π²)]¹/³

Calculating this expression, we find:

r = 2.043 x 10⁷ meters

Therefore, the satellite orbits Mars at a radius of approximately 2.043 x 10⁷ meters

Read mroe on the orbit of satellite here

https://brainly.com/question/18496962

#SPJ1

Answer:

2.5

Explanation:

quiz

We can show that  the elastic collision V₁ = 2m₂U₂ + U₁(m₁ - m₂)/(m₁ + m₂).

m₁u₁ + m₂U₂ = M₁V₁ + m₂v₂ to solve for V₁.

m₁u₁ + m₂U₂ = M₁V₁ + m₂v₂

M₁V₁ = m₁u₁ + m₂U₂ - m₂v₂

M₁V₁ = m₁u₁ + m₂U₂ - m₂(V₁ + U₁ - U₂)

expand and combine like terms

(M₁ + m₂)V₁ = m₁u₁ - m₂V₁ + m₂U₂ + m₂U₂ - m₂U₁

(M₁ + m₂)V₁ + m₂V₁ = m₁u₁ + 2m₂U₂ - m₂U₁

We then factor out V₁:

(V₁(M₁ + m₂) + m₂V₁) = m₁u₁ + 2m₂U₂ - m₂U₁

V₁(M₁ + m₂ + m₂) = m₁u₁ + 2m₂U₂ - m₂U₁

V₁(M₁ + 2m₂) = m₁u₁ + 2m₂U₂ - m₂U₁

Dividing both sides by (M₁ + 2m₂):

V₁ = (m₁u₁ + 2m₂U₂ - m₂U₁) / (M₁ + 2m₂

V₁ = (m₁u₁ + 2m₂U₂ - m₂U₁)(m₁ - m₂)/(m₁ - m₂) / (M₁ + 2m₂)

V₁ = (u₁m₁m₂ + m₂(2U₂m₂ - U₁m₂)) / (m₂(M₁ + m₂))

V₁ = (u₁m₁m₂ + m₂(2U₂m₂ - U₁m₂)) / (m₂M₁ + m₂²)

We then factori ot m₂ from the numerator:

V₁ = m₂(u₁m₁ + 2U₂m₂ - U₁m₂) / (m₂M₁ + m₂²)

V₁ = 2m₂U₂ + U₁(m₁ - m₂) / (m₁ + m₂)

Learn more about elastic Collison at:

https://brainly.com/question/12644900

#SPJ1

The relative velocity of the two cars moving along a straight path with the same velocity is zero.

The relative velocity of an object is defined as the velocity of the object with respect to another observer.

If the two cars are moving along a straight path with the same velocity, their relative velocity would be zero.

Mathematically, the formula is given as;

Vr = Va - Vb

where;

Va is the velocity of car A

Vb is the velocity of car B

Since both cars have the same velocity, the relative velocity is calculate das;

Va = Vb

Vr = Va - Va

Vr = 0 m/s

Thus, the relative velocity of the two cars moving along a straight path with the same velocity is zero.

Learn  more about relative velocity here: https://brainly.com/question/17228388

#SPJ1