Answer:
A) K / K₀ = 4 b) v / v₀ = 4
Explanation:
A) For this exercise we can use the conservation of mechanical energy
in the problem it indicates that the displacement was doubled (x = 2xo)
starting point. At the position of maximum displacement
Em₀ = Ke = ½ k (2x₀)²
final point. In the equilibrium position
= K = ½ m v²
Em₀ = Em_{f}
½ k 4 x₀² = K
(½ K x₀²) = K₀
K = 4 K₀
K / K₀ = 4
B) the speed value
½ k 4 x₀² = ½ m v²
v = 4 (k / m) x₀
if we call
v₀ = k / m x₀
v = 4 v₀
v / v₀ = 4
1) Velocity: 9.9 m/s and 14 m/s
The motion of the diver is a free-fall motion, so it is a uniform accelerated motion. Choosing downward as positive direction, the final velocity can be found by using the following suvat equation:
where
v is the final velocity
u = 0 is the initial velocity (the diver starts from rest)
is the acceleration of gravity
s is the displacement
For the diver jumping from 5 m, s = 5 m, so
For the diver jumping from 10 m, s = 10 m, so
2) Time: 1.01 s and 1.43 s
The time of flight of each diver can be found by using the other suvat equation
And since u = 0, it can be reduced to
For the diver jumping from 5 m, s = 5 m, so we find
For the diver jumping from 10 m, s = 10 m, so we find