Answer:
Her altitude as she crosses the bar, h₂ is approximately 6.1 m
Explanation:
The given parameters of the motion of the pole vaulter are;
The mass of the pole vaulter, m = 57 kg
The speed with which the pole vaulter is running, u = 11 m/s
The speed of the pole vaulter when she crosses the bar, v = 1.1 m/s
The acceleration due to gravity, g = 9.8 m/s²
From the total mechanical energy, M.E. equation, we have;
M.E. = P.E. + K.E.
Where;
P.E. = The potential energy of the motion = m·g·h
K.E. = The kinetic energy of the motion = 1/2·m·v²
By the principle of conservation of energy, we have;
The change (loss) in kinetic energy, ΔK.E. = The change (gain) in potential energy, ΔP.E.
ΔK.E. = 1/2·m·(v² - u²)
ΔP.E. = m·g·(h₂ - h₁)
Where;
h₁ = The ground level = 0 m
h₂ = The altitude with which she crosses the bar
∴ 1/2·m·(v² - u²) = m·g·(h₂ - h₁)
(h₂ - h₁) = (v² - u²)/(2·g) = (11² - 1.1²)/(2·9.8) = 6.11173469388
h₂ = 6.11173469388 + h₁ = 6.11173469388 + 0 = 6.11173469388
h₂ = 6.11173469388
Her altitude as she crosses over the bar, h₂ ≈ 6.1 m.
