Respuesta :
m = mass of trampoline artist = 65 kg
v₀ = initial speed of the artist at the top of platform = 5 [tex]\frac{m }{s}[/tex]
h = height through which the artist drop before landing on trampoline = 3 m
v = final speed of the artist just before landing on trampoline = ?
using conservation of energy
Kinetic energy of artist just before landing = initial kinetic energy at the top of platform + potential energy at the top of platform
(0.5) m v² = (0.5) m v₀² + mgh
dividing each term by "m"
(0.5) v² = (0.5) v₀² + gh
inserting the values
(0.5) v² = (0.5) (5)² + (9.8)(3)
v = 9.2 [tex]\frac{m }{s}[/tex]
x = compression of the trampoline = ?
k = spring stiffness constant = 62000 [tex]\frac{N }{m}[/tex]
Assuming the lowest depression point as reference line for measuring the potential energy
using conservation of energy
kinetic energy of artist + potential energy of artist before landing = spring potential energy of trampoline
(0.5) m v² + mg x = (0.5) k x²
inserting the values
(0.5) (65) (9.2)² + (65 x 9.8) x = (0.5) (62000) x²
x = 0.31 m
Answer:
The length of depress is [tex]0.31\;\rm{m[/tex].
Explanation:
Given: A [tex]65\;\rm{kg}[/tex] trampoline artist jumps vertically upward from the top of a platform with a speed of [tex]5\;\rm{m/s[/tex].
So, using conservation of energy
Kinetic energy of artist just before landing = initial kinetic energy at the top of platform + potential energy at the top of platform
[tex]\frac{1}{2}mv^2=\frac{1}{2}mv_{o}^2+mgh\\[/tex]
Dividing whole equation by [tex]'m'[/tex]
[tex]0.5v^2=0.5\times5^2+9.8\times3\\\\0.5v^2=41.9\\[/tex]
[tex]v^2=\frac{41.9}{0.5}\\v^2=83.8\\\;\;\;\; v=9.2\;\rm{m/s}[/tex]
Let [tex]x[/tex] be the compression of the trampoline.
Again using the conservation of energy formula:
[tex]\frac{1}{2}kx^2=\frac{1}{2}mv}^2+mgx\\\\0.5\times6.2\times10^4\times{x^2=0.5\times65\times(9.2)^2+65\times9.8\times{x}\\31000{x}^2=2750.8+637x\\31000{x}^2-637x-2750.8=0[/tex]
By solving the quadratic equation: [tex]x=0.31\;\rm{m[/tex]
Hence, the length of depress is [tex]0.31\;\rm{m[/tex].
Learn more about conservation of energy here: https://brainly.com/question/22536824?referrer=searchResults
