Question

The hull speed of a boat is approximated by the function

v = 1.34 StartRoot l EndRoot ,

where l is the hull length in feet and v is the hull speed in knots.

Suppose the Santa Monica has a hull length that is 10 ft shorter than that of the Nina Pinta. What expression represents the hull speed of the Santa Monica in terms of the length, ln of the Nina Pinta?

v Subscript s Baseline = a StartRoot b EndRoot

Where a =
and b = ln

What are the restrictions on ln?

ln >

Answer 1

v_s = 1.34 sqrt(l_n - 10)

So a = 1.34 and b = l_n - 10.

Restriction: l_n - 10 ≥ 0, so l_n ≥ 10 (physically, l_n > 10 if you require a positive length), typically written as l_n > 10.