A swimming pool of a width 90m and length 24m is filled with water to a depth of 30m. Calculate pressure on the bottom of the pool due to the water.
Answers
Given :
- length and width of pool as 24 m and 90 m respectively.
- pool is filled to a depth, h = 30 m
To find :
- Pressure on the bottom of the pool due to water, P = ?
Knowledge required :
Pressure exerted by any fluid due to the force of gravity, at an equilibrium when it is in rest is known as Hydrostatic of fluid pressure.
Formula to calculate Fluid pressure
- P = ρ g h
[ where P is fluid pressure, ρ is density of given fluid, g is acceleration due to gravity and h is height ]
Calculation :
- density of water, ρ = 997 kg / m³
- depth of water in pool, h = 30 m
- acceleration due to gravity, g = 9.8 m/s²
Using formula for fluid pressure
→ P = ρ g h
→ P = 997 × 9.8 × 30
→ P = 293118 Pascal
therefore,
pressure on the bottom of the pool due to water is 293118 Pascals.
Answer:
a) V₀ = 13.5m/s
a) V₀ = 13.5m/sb) a = 2.1 m/s²
Explanation:-
1) Convert velocities to m/s
i) 20 km/h × 1000m/kg × 1h/3600s = 5.556m/s
ii) 40km/h = 11.111m/s
2) Red car, time elapsed to reach position x = 44.5m
Constant velocity ⇒ x = V×t ⇒ t = x / V
⇒ t₁ = 44.5m / 5.556m/s = 8s
3) Red car, time elapsed to reach position x = 77.6m
t₂ = 76.6m / 11.111/s = 6.9s
4) Green car, distance run at t₁ = 8s, x = 44.5m
i) uniform acceleration equation d = V₀t + at² / 2
ii) d = 220m - x = 220m - 44.5m = 175.5m = V₀ (8) + a (8)² /2
175.5 = 8V₀ + 32a ↔ equation (1)
5) Green car, distance run at t₂ = 6.9s, x = 76.6m
i) d = 220m - x = 220m - 76.6m = 143.4
ii) 143.4 = V₀t₂ + at₂² / 2
143.4 = V₀ (6.9) + a(6.9)² / 2
143.4 = 6.9V₀ + 23.8a ↔ equation (2)
6) Solve the system of equations:
175.5 = 8V₀ + 32a ↔ equation (1)
143.4 = 6.9V₀ + 23.8a ↔ equation (2)
V₀ = 13.5m/s
a = 2.1 m/s²
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