Final answer:
To calculate the pressure at the depth of the Mariana Trench, use the pressure equation P = ρgh + P0. With the given constants, the pressure a submarine must withstand to reach this depth is approximately 1.118 × 10^8 Pa.
Step-by-step explanation:
To calculate the pressure that a submarine would need to withstand at the depth of the Mariana Trench, one can use the equation for pressure due to a fluid column, which is P = ρgh + P0, where ρ is the density of the fluid (sea water in this case), g is the acceleration due to gravity, h is the height (or depth) of the fluid column, and P0 is the atmospheric pressure at the surface level.
Given the density of seawater (ρ) as 1025 kg/m3, acceleration due to gravity (g) as 9.81 m/s2, depth (h) of the Mariana Trench as 11,000 m (since 1 km = 1000 m), and the atmospheric pressure at sea level (P0) as 1.01 × 105 Pa, we can calculate the pressure using these values.
The pressure due to the ocean at the given depth is:
P = 1025 kg/m3 × 9.81 m/s2 × 11,000 m + 1.01 × 105 Pa
P = 1.117 × 108 Pa + 1.01 × 105 Pa
= 1.118 × 108 Pa (approx)
A submarine would need to be able to withstand a pressure of approximately 1.118 × 108 Pa to reach the bottom of the Mariana Trench.