Exercise 3 Page 290

Practice makes perfect

a By substituting the number of people into the formula, we can calculate the speed of the boat. Note that we need a calculator for this.

rowers	4.62sqrt(n)	s
n= 2	4.62sqrt(2)	≈ 5.0
n= 4	4.62sqrt(4)	≈ 5.4
n= 8	4.62sqrt(8)	≈ 5.8

b If we call the smaller number of people n= P, then twice this number can be expressed as n= 2P. With this, we can write two expressions for the speed of the boat when it holds the different number of rowers.

P rowers:& s_P = 4.62sqrt(P) 2P rowers:& s_(2P) = 4.62sqrt(2P) To compare the different speeds, we divide the expression for the speed of the boat with the greater number of rowers, with the expression for the speed of the boat with the lower number of rowers. The quotient will tell us how many times the speed increases when the rowers double.

S_(2P)/S_P

SubstituteII

S_(2P)= 4.62sqrt(2P), S_P= 4.62sqrt(P)

4.62sqrt(2P)/4.62sqrt(P)

▼

Simplify

SqrtProd

sqrt(a* b)=sqrt(a)*sqrt(b)

4.62sqrt(2)sqrt(P)/4.62sqrt(P)

ReduceFrac

a/b=.a /4.62sqrt(P)./.b /4.62sqrt(P).

sqrt(2)

UseCalc

Use a calculator

1.08006...

RoundDec

Round to 2 decimal place(s)

≈ 1.08

The boat with twice the number of rowers goes about 8 % faster than the less crowded boat.

c From Part A, we know the speed that the boat travels when it has the different number of rowers.

2 rowers:& s=5.0 mps 4 rowers:& s≈ 5.4 mps 8 rowers:& s≈ 5.8 mps By dividing the length of the race by these speeds, we can find the time it takes for each boat to complete it

rowers	speed	2000/s	time
2	s= 5	2000/5	400 s
4	s≈ 5.4	2000/5.4	≈ 370 s
8	s≈ 5.8	2000/5.8	≈ 344 s

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Exercises p.290-291

Exercise 3 Page 290

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