According to the law of conservation of energy at the highest point of the roller coaster ride, that is, the hill, the whole (maximum) kinetic energy of the roller coaster is converted into its potential energy:

$Maximum\ Kinetic\ Energy\ Lost = Maximum\ Potential\ Energy\ Gain\\\\
\frac{1}{2}mv_{max}^2=mgh\\\\
h=\frac{v_{max}^2}{2g}$

where,

h = height of the hill = ?

$v_{max}$ = maximum velocity = 57.2 m/s

g = acceleration due to gravity = 9.81 m/s²

Therefore,

$h=\frac{(57.2\ m/s)^2}{2(9.81\ m/s^2)}\\\\
$

Learn more about the law of conservation of energy here:

brainly.com/question/101125

7 0

3 years ago

When the hydrogen atom makes the transition from the n=2 to the n=1 energy level, it emits a photon. This photon can be absorbed

bazaltina [42]

Answer:

$n_{fn}$ = 4

Explanation:

To solve this exercise we will use Bohr's atomic model

$E_{n}$ = - 13.606 / n² [eV]

The transition from level n = 2 to level n = 1 is valid

$E_{21}$ = - 13.606 [¼ -1/1]

$E_{21}$ = 10.2045 eV

Bohr's model for atoms with only one electron is

$E_{n}$ = -13.606 Z² / n²

Where Z is the atomic number of the atom.

In this case the helium atom has an atomic number of Z = 2 from the level n₀ = 2 let's look up to what level it reaches

ΔE = -13.606 [4 / $n_{fn}$ ² - 4/4]

4 / $n_{fn}$ ² = -ΔE / 13.606 + 1

4 / $n_{fn}$ ² = -10.2045 / 13.606 +1 = -0.75 +1

4 / $n_{fn}$ ² = 0.25

$n_{fn}$ = √ 4 / 0.25

$n_{fn}$ = 4

8 0

3 years ago