Answer:
9.54 cm
Explanation:
The water is in free fall after it leaves the tank. The time it takes to land is:
Δy = v₀ t + ½ at²
1.23 m = (0 m/s) t + ½ (9.8 m/s²) t²
t = 0.501 s
Therefore, the horizontal velocity is:
v = 0.685 m / 0.501 s
v = 1.37 m/s
Using Bernoulli equation, where point 1 is the surface of the water and point 2 is the exit of the tank:
P₁ + ½ ρ v₁² + ρgh₁ = P₂ + ½ ρ v₂² + ρgh₂
Since P₁ = P₂, and v₁ = 0:
ρgh₁ = ½ ρ v₂² + ρgh₂
gh₁ = ½ v₂² + gh₂
gh = ½ v₂²
h = v₂²/(2g)
Plugging in:
h = (1.37 m/s)² / (2 × 9.8 m/s²)
h = 0.0954 m
h = 9.54 cm
