Because the more advances made in the world means the more we can learn on how things work and how we can better the lives of humans and other species. If we didn't have scientific advancements we wouldn't have cell phones, electric, tv, car, computers, ect. We would still be living in Cave man era with clubs and horrible language skills.
<h2>Question:</h2>
In this circuit the resistance R1 is 3Ω, R2 is 7Ω, and R3 is 7Ω. If this combination of resistors were to be replaced by a single resistor with an equivalent resistance, what should that resistance be?
Answer:
9.1Ω
Explanation:
The circuit diagram has been attached to this response.
(i) From the diagram, resistors R1 and R2 are connected in parallel to each other. The reciprocal of their equivalent resistance, say Rₓ, is the sum of the reciprocals of the resistances of each of them. i.e

=>
------------(i)
From the question;
R1 = 3Ω,
R2 = 7Ω
Substitute these values into equation (i) as follows;


Ω
(ii) Now, since we have found the equivalent resistance (Rₓ) of R1 and R2, this resistance (Rₓ) is in series with the third resistor. i.e Rₓ and R3 are connected in series. This is shown in the second image attached to this response.
Because these resistors are connected in series, they can be replaced by a single resistor with an equivalent resistance R. Where R is the sum of the resistances of the two resistors: Rₓ and R3. i.e
R = Rₓ + R3
Rₓ = 2.1Ω
R3 = 7Ω
=> R = 2.1Ω + 7Ω = 9.1Ω
Therefore, the combination of the resistors R1, R2 and R3 can be replaced with a single resistor with an equivalent resistance of 9.1Ω
In general, that's not possible, unless the three numbers relate to
very specific quantities.
For example, if the three numbers are the object's height, temperature,
and cost, then they are of no help at finding the object's velocity.
Answer:
12.5 m/s
Explanation:
From the question given above, the following data were obtained:
Initial velocity (u) = 0 m/s
Height (h) = 8 m
Final velocity (v) at 8 m above the lowest point =?
NOTE: Acceleration due to gravity (g) = 9.8 m/s²
The velocity of the roller coaster at 8 m above the lowest point can be obtained as follow:
v² = u² + 2gh
v² = 0² + (2 × 9.8 × 8)
v² = 0 + 156.8
v² = 156.8
Take the square root of both side
v = √156.8
v = 12.5 m/s
Therefore, the velocity of the roller coaster at 8 m above the lowest point is 12.5 m/s.
Answer:
6 m/s is the missing final velocity
Explanation:
From the data table we extract that there were two objects (X and Y) that underwent an inelastic collision, moving together after the collision as a new object with mass equal the addition of the two original masses, and a new velocity which is the unknown in the problem).
Object X had a mass of 300 kg, while object Y had a mass of 100 kg.
Object's X initial velocity was positive (let's imagine it on a horizontal axis pointing to the right) of 10 m/s. Object Y had a negative velocity (imagine it as pointing to the left on the horizontal axis) of -6 m/s.
We can solve for the unknown, using conservation of momentum in the collision: Initial total momentum = Final total momentum (where momentum is defined as the product of the mass of the object times its velocity.
In numbers, and calling
the initial momentum of object X and
the initial momentum of object Y, we can derive the total initial momentum of the system: 
Since in the collision there is conservation of the total momentum, this initial quantity should equal the quantity for the final mometum of the stack together system (that has a total mass of 400 kg):
Final momentum of the system: 
We then set the equality of the momenta (total initial equals final) and proceed to solve the equation for the unknown(final velocity of the system):
