Ability of the muscles to function effectively and efficiently without undue fatigue

Answer

Given data:

height of the dam = 15 m

effective area for water flow = 2.3 x 10⁻³ m²

Applying the principle of energy conservation:

v = 17.15 m/s

water discharge

Q = A V

Q = 2.3 x 10⁻³ x 17.15

Q = 0.039 m³/s

Since the absolute values of the charges are identical, the changes in potential energy remain equivalent. Consequently, the changes in kinetic energy will also match. We have:

1 = Ke/Kp = m_e * v_e^2 / m_p * v_p^2, which simplifies to:

v_e/v_p = sqrt(m_p/m_e),

indicating that the velocity of the electron is sqrt(m_p/m_e) times greater than that of the proton.

a) The student's speed after jumping is 1.07 m/s

b) The final speed of the laser is 10.4 m/s

Explanation:

a)

This issue can be approached through the momentum conservation principle: In the absence of external forces, the combined momentum of the student and the laser must remain unchanged. Hence, we can express:

where:

The initial momentum is zero

m = 42 kg signifies the mass of the laser

v = 1.5 m/s is the laser's final velocity

M = 59 kg is the mass of the student

V denotes the student's final velocity

Solving this for V, we can determine the student's speed:

Thus, the student's final speed calculates to 1.07 m/s.

b)

Here, both the laser and the student have a combined speed of 3.1 m/s prior to the student's jump; thus, the initial momentum isn't zero.

<pSo, we formulate the equation of momentum conservation as:

where:

m = 42 kg denotes the mass of the laser

M = 59 kg is the student’s mass

u = 3.1 m/s is their starting velocity

V = -2.1 m/s indicates the student's speed post-jump (she jumps backward)

v signifies the laser's final speed

When we resolve for v, we have:

Learn more about momentum: