Question

Starting at sea level, a submarine descended at a constant rate to a depth of −3/4 mile relative to sea level in 5/8 minutes.

Answer 1

The submarine's depth relative to sea level after the first minute is 1.2 miles

How to find the submarine's depth relative to sea level after the first minute?

To find the submarine's depth after the first minute, we first need to find the rate at which the submarine descends, r.

The rate at which the submarime descends is r = d/t where

• d = submarine's depth and
• t = time of descent to depth d.

Given that submarine descended at a constant rate to a depth of −3/4 mile relative to sea level in 5/8 minutes, we have that

• d = -3/4 mile and
• t = 5/8 minutes.

So, substituting these into r, we have

r = d/t

= -3/4 mile ÷ 5/8 min

= -3/4 × 8/5

= -3 × 2/5

= -6/5

= -1.2 mile/min

So, the depth of the submarine after the first minute is given by D = rt where r = rate of descent =  -1.2 mile/min and t = time = 1 min

So, substituting these into D, we have

D = rt

=  -1.2 mile/min × 1 min

= -1.2 mile

So, the submarine's depth relative to sea level after the first minute is 1.2 miles

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