A person on a trampoline bounces straight upward with an initial speed of 4.7m/s . What is the magnitude of the person's speed when she returns to her initial height?

Check your 10:47pm post for solution.

To find the magnitude of the person's speed when she returns to her initial height, we can apply the principle of conservation of mechanical energy.

The principle of conservation of mechanical energy states that the total mechanical energy (kinetic energy + potential energy) of a system remains constant if no external forces are acting on it.

In this case, as the person is bouncing on a trampoline, we can assume that no external forces such as air resistance or friction are acting on the person.

At the initial height, the person has both kinetic energy (due to upward motion) and potential energy (due to height from the ground). Therefore, the total mechanical energy is given by:

E_initial = Kinetic energy_initial + Potential energy_initial

At maximum height, the person's velocity is momentarily zero, so the kinetic energy is zero. The potential energy is at its maximum because the person is at the highest point. Therefore, the total mechanical energy at the maximum height is:

E_max = Kinetic energy_max + Potential energy_max

Since mechanical energy is conserved, the initial mechanical energy is equal to the maximum mechanical energy:

E_initial = E_max

Substituting the formulas for kinetic and potential energy, we have:

1/2 m v_initial^2 + m g h_initial = 1/2 m v_max^2 + m g h_max

Where:
m = mass of the person
v_initial = initial velocity (4.7 m/s)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h_initial = initial height (0 m, as the person starts at the ground)
h_max = maximum height reached

Rearranging the equation to solve for v_max (the magnitude of the person's velocity at maximum height):

1/2 m v_max^2 = 1/2 m v_initial^2 + m g h_initial - m g h_max

v_max^2 = v_initial^2 + 2 g (h_initial - h_max)

Taking the square root of both sides, we get:

v_max = √(v_initial^2 + 2 g (h_initial - h_max))

Substituting the given values into the equation:

v_max = √(4.7^2 + 2 * 9.8 * (0 - h_max))

Now, to find the magnitude of the person's velocity when she returns to her initial height, we need to find the maximum height reached by the person on the trampoline.

Unfortunately, the given problem statement does not provide information about the maximum height reached by the person. Hence, it is not possible to determine the final answer without knowing the maximum height.

To find the magnitude of the person's velocity when she returns to her initial height, you need to know the maximum height reached by the person on the trampoline.