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3 years ago

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A rabbit hops through a vegetable garden. He first hops 2 m south, then 4 m west, then 3 m south, and finally 1 m east. What dis

tance did the rabbit travel? What is his displacement?

1 answer:

Semenov [28]3 years ago

7 0

Answer:

Distance = 10m

Imagine a triangle

Length = 4 - 1 = 3

Height = 2 + 2 =4

Hypothenuse = Displacement

Displacement = 5

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An electron in the n = 7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 397 nm. what is the value

Dimas [21]

Answer:

$n_f=2$

Explanation:

It is given that,

Initially, the electron is in n = 7 energy level. When it relaxes to a lower energy level, emitting light of 397 nm. We need to find the value of n for the level to which the electron relaxed. It can be calculate using the formula as :

$\dfrac{1}{\lambda}=R(\dfrac{1}{n_f^2}-\dfrac{1}{n_i^2})$

$\dfrac{1}{397\times 10^{-9}\ m}=R(\dfrac{1}{n_f^2}-\dfrac{1}{(7)^2})$

R = Rydberg constant, $R=1.097\times 10^7\ m^{-1}$

$\dfrac{1}{397\times 10^{-9}\ m}=1.097\times 10^7\ m^{-1}\times (\dfrac{1}{n_f^2}-\dfrac{1}{(7)^2})$

Solving above equation we get the value of final n is,

$n_f=2.04$

or

$n_f=2$

So, it will relax in the n = 2. Hence, this is the required solution.

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A train is moving at 15ms-1. It slows down to 10.5ms over a time of 4s. Calculate the distance it travels before stopping if acc

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3 years ago

Use the law of conservation of energy (assume no friction nor air resistance) to determine the kinetic and potential energy at t

slava [35]

Answer:

Part A

1) At the starting point, we have;

PE = 40,000 J

2) PE = 0 J, KE = 40,000 J

3) KE = 20,000 J

4) PE = 15,000 J

5) KE = 32,500 J

6) KE = 40,000 J, PE = 0 J

7) KE = 35,000 J

8) KE = 40,000 J, PE = 0 J

Part B

The total Mechanical Energy = ME = 40,000 J

At the final point, we have;

ME = KE + PE = 40,000 J + 0 J = 40,000 J

Explanation:

Part A

By the law of conservation of energy, we have;

ME = PE + KE

Where;

ME = The total Mechanical Energy of the system

PE = The Potential Energy of the system

KE = The Kinetic Energy of the system

Where there is no friction, we have;

At the final stage, KE = 40,000 J. PE = 0 J

Therefore, ME = PE + KE = 40,000 J + 0 J = 40,000 J

1) At the starting point, we have;

KE = 0 J, therefore, PE = ME - KE = 40,000 J - 0 J = 40,000 J

2) At the bottom of the roller coaster, at the same level the PE is taken as PE = 0 J at the final stage, we have;

PE = 0 J, therefore, KE = ME - PE = 40,000 J - 0 J = 40,000 J

3) Where PE = 20,000 J, KE = ME - PE = 40,000 J - 20,000 J = 20,000 J

4) Where KE = 25,000 J, PE = ME - KE = 40,000 J - 25,000 J = 15,000 J

5) Where PE = 7,500 J, KE = ME - PE = 40,000 J - 7,500 J = 32,500 J

6) At the bottom KE = 40,000 J, PE = 0 J

7) Where PE = 5,000 J, KE = ME - PE = 40,000 J - 5,000 J = 35,000 J

8) KE = 40,000 J, PE = 0 J

Part B

The given that there is no friction nor air resistance, the total Mechanical Energy, ME, is constant and equal to the sum of the Potential Energy, PE and the Kinetic Energy, KE, as follows;

ME = KE + PE

At the final point, we have;

ME = 40,000 J + 0 J = 40,000 J

The total Mechanical Energy = ME = 40,000 J

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The computation would be:moles = mass/ Molar Mass, but we are looking for the mass, so rearranging, will give us: mass = moles x MM
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Q = (mass/MM) x Hf
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= (1.50-kJ x 18.0-g/mol) / 6.01-kJ/mol
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