Solution_CP1.pdf - ESO208A Class Problem 1 Problem A ball was dropped from rest at a measured height of H m and the time tH it takes to reach the ground

# Solution_CP1.pdf - ESO208A Class Problem 1 Problem A ball...

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ESO208A: Class Problem 1 Problem: A ball was dropped from rest at a measured height of H m and the time t H it takes to reach the ground was recorded. If H = 660 ± 0.01 m and time t = 11.65 ± 0.01 s. Find an estimate of the acceleration due to gravity g. Solution: Governing equation: d 2 h dt 2 = g Initial condition: t=0, h=0, dh dt = 0 dh dt = gt + a h = 0.5gt 2 + at + b (2 marks) Applying initial condition, a=b=0 h=0.5gt 2 fሺh, tሻ ൌ g ൌ 2h t g= 9.726 (1 mark)

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Unformatted text preview: ∂f ∂h = 2 t 2 ∂f ∂t =-4h t 3 t ̃ = t ± Δt (t=11.65, Δt = 0.01) h ෨ ൌhേΔh (h=660, Δh = 0.01) g ෤ൌgേΔg Applying propagation of error concept using first order approximation, Δg= ฬ ∂f ∂t Δt ฬ + ฬ ∂f ∂h Δh ฬ Δg= 1.67*0.01 ൅ 0.0147*0.01 (considering infinite precision for intermediate calculations) (3 marks) = 0.0168 ൎ 0.02 (2 marks) gേΔg ൎ 9.73 േ 0.02 m/s 2 (1+1 marks)...
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