Question

6. The flight deck of the U.S.S. Nimitz is about 60 ft above the water, depending on load. If a member of the flight deck crew falls into the water and reaches a depth of 45 ft, estimate the average force exerted by the water on them. (assume a constant force)

Answer 1

Using Energy conservation between Initial and final point:

KEi + PEi + Wr = KEf + PEf

KEi = 0 J, since initial speed of person is 0 m/sec

PEf = 0 J, Gravitational PE at depth of 45 ft, assuming it as reference point

PEi = m*g*H, where H = height of person from reference point = 105 ft = 32.004 m

KEf = 0, since final speed is zero, So

0 + m*g*H + Wr = 0 + 0

Wr = Work-done by resistive force of water = -Fr*d (-ve sign means resistive force is in opposite direction of motion)

d = distance traveled in water = 45 ft =13.716 m

So,

Wr = -m*g*H

-Fr*d = -m*g*H

Fr = Average force exerted by water = m*g*H/d

Here I believe we've to assume average mass of crew member = approx 70 kg (If this value is mentioned by your TA, then let me know), So

Fr = 70*9.81*32.004/13.716

Fr = 1602.3 N

Let me know if you've any query.