To launch a 100 kg human with a velocity of 4 m/s using a spring, we can use the conservation of energy.
The energy stored in the spring when it is compressed is given by:
E = 1/2 kx^2
where k is the spring constant, x is the compression of the spring from its natural length.
The total energy required to launch the person is the sum of the potential energy stored in the compressed spring and the kinetic energy of the person after being launched. This is given by:
E = 1/2 mv^2
where m is the mass of the person, and v is the velocity at which the person is launched.
Since energy is conserved, we can equate the two expressions for energy:
1/2 kx^2 = 1/2 mv^2
Substituting the given values, we get:
1/2 k(2.0 m)^2 = 1/2 (100 kg)(4 m/s)^2
Simplifying the equation, we get:
k = (100 kg)(4 m/s)^2 / (2.0 m)^2 = 1600 N/m
Therefore, the spring constant required to launch the person is 1600 N/m. The correct answer is o 1600 N/m.