Potential energy can be calculated using the following rule:
potential energy = mgh where:
m is the mass = 85 kg
g is the acceleration due to gravity = 9.8 m/sec^2
h is the height = 4 km = 4000 meters
Substitute in the above equation to get the potential energy as follows:
Potential energy = 85*9.8*4000 = 3332000 joules
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Recall the equation for centripetal force:

We can rearrange the equation to solve for 'r'.
Multiply both sides by r:

Divide both sides by Fc:

Answer:
(a) The energy of the photon is 1.632 x
J.
(b) The wavelength of the photon is 1.2 x
m.
(c) The frequency of the photon is 2.47 x
Hz.
Explanation:
Let;
= -13.60 ev
= -3.40 ev
(a) Energy of the emitted photon can be determined as;
-
= -3.40 - (-13.60)
= -3.40 + 13.60
= 10.20 eV
= 10.20(1.6 x
)
-
= 1.632 x
Joules
The energy of the emitted photon is 10.20 eV (or 1.632 x
Joules).
(b) The wavelength, λ, can be determined as;
E = (hc)/ λ
where: E is the energy of the photon, h is the Planck's constant (6.6 x
Js), c is the speed of light (3 x
m/s) and λ is the wavelength.
10.20(1.6 x
) = (6.6 x
* 3 x
)/ λ
λ = 
= 1.213 x 
Wavelength of the photon is 1.2 x
m.
(c) The frequency can be determined by;
E = hf
where f is the frequency of the photon.
1.632 x
= 6.6 x
x f
f = 
= 2.47 x
Hz
Frequency of the emitted photon is 2.47 x
Hz.
A 100kg crate slides along a floor with a starting velocity of 21 m/s. If the force due to friction is 8N, then, it will take 262.5 s for the box to come to rest.
We'll begin by calculating the declaration of the box. This can be obtained as follow:
Force (F) = –8 N (opposition)
Mass (m) = 100 Kg
<h3>Deceleration (a) =? </h3>
<h3>F = ma</h3>
–8 = 100 × a
Divide both side by 1000

<h3>a = –0.08 ms¯²</h3>
Therefore, the deceleration of the box is –0.08 ms¯²
Finally, we shall determine the time taken for the box to come to rest. This can be obtained as follow:
Deceleration (a) = –0.08 ms¯²
Initial velocity (u) = 21 ms¯¹
Final velocity (v) = 0 ms¯¹
<h3>Time (t) =.? </h3>
<h3>v = u + at</h3>
0 = 21 + (–0.08×t)
0 = 21 – 0.08t
Collect like terms
0 – 21 = –0.08t
–21 = –0.08t
Divide both side by –0.08

<h3>t = 262.5 s</h3>
Therefore, it will take 262.5 s for the box to come to rest.
Learn more: brainly.com/question/14446351