The concept needed to solve this problem is average power dissipated by a wave on a string. This expression ca be defined as

Here,
= Linear mass density of the string
Angular frequency of the wave on the string
A = Amplitude of the wave
v = Speed of the wave
At the same time each of this terms have its own definition, i.e,
Here T is the Period
For the linear mass density we have that

And the angular frequency can be written as

Replacing this terms and the first equation we have that



PART A ) Replacing our values here we have that


PART B) The new amplitude A' that is half ot the wavelength of the wave is


Replacing at the equation of power we have that


Answer:
xf = 5.68 × 10³ m
yf = 8.57 × 10³ m
Explanation:
given data
vi = 290 m/s
θ = 57.0°
t = 36.0 s
solution
firsa we get here origin (0,0) to where the shell is launched
xi = 0 yi = 0
xf = ? yf = ?
vxi = vicosθ vyi = visinθ
ax = 0 ay = −9.8 m/s
now we solve x motion: that is
xf = xi + vxi × t + 0.5 × ax × t² ............1
simplfy it we get
xf = 0 + vicosθ × t + 0
put here value and we get
xf = 0 + (290 m/s) cos(57) (36.0 s)
xf = 5.68 × 10³ m
and
now we solve for y motion: that is
yf = yi + vyi × t + 0.5 × ay × t
² ............2
put here value and we get
yf = 0 + (290 m/s) × sin(57) × (36.0 s) + 0.5 × (−9.8 m/s2) × (36.0 s) ²
yf = 8.57 × 10³ m
The Earth's core is estimated to be bigger than both Mars and Mercury. However, I would say that Mercury is the safest choice. Mercury is also known to be smaller than Jupiter's Moon!