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m = mass of trampoline artist = 65 kg
v₀ = initial speed of the artist at the top of platform = 5
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
x = compression of the trampoline = ?
k = spring stiffness constant = 62000
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