Exercise 47 Page 689

We are given that Jonas is swimming from the east bank to the west bank of a stream at a speed of 3.3 feet per second, and we know that the stream is 80 feet wide, flows south, and that Jonas crosses this stream in 20 seconds. First, let's evaluate the resultant speed using the given information. Resultant speed:80/20=4 The resultant speed is 4 feet per second. Now we can sketch a diagram describing the given situation. Let vector c represents the speed of the current.

Let's notice that the vectors form a right triangle as the vector describing Jonas' speed is perpendicular to the vector describing the current's speed.

Therefore, we can solve for c using the Pythagorean Theorem. According to this theorem, the sum of the squared legs of a right triangle is equal to its squared hypotenuse. c^2+ 3.3^2=4^2 Let's solve the above equation to find the speed of the current. Notice that since c represents a speed, we will consider only the positive case when taking a square root of c^2.

c^2+3.3^2=4^2

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Solve for c

CalcPow

Calculate power

c^2+10.89=16

SubEqn

LHS-10.89=RHS-10.89

c^2=5.11

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(c^2)=sqrt(5.11)

SqrtPowToNumber

sqrt(a^2)=a

c=sqrt(5.11)

UseCalc

Use a calculator

c=2.2605...

RoundDec

Round to 1 decimal place(s)

c≈ 2.3

The speed of the current is approximately 2.3 feet per second.