# The speed of the boat with wetted surface area 28 ft 2 and drag force is 175 lb . ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.11, Problem 39E
To determine

## To find: The speed of the boat with wetted surface area 28 ft2 and drag force is 175 lb.

Expert Solution

The speed of the boat is 5.33mi/h.

### Explanation of Solution

Given:

The condition is, FAs2. Here F is the drag force on the boat, A is the wetted surface area on the hull and s is the speed of the boat.

Initially boat experienced a drag force of 220lb with the wetted surface area of 40ft2 and speed of 5mi/h.

Calculation:

From the given condition, FAs2.

That is,

F=kAs2 (1)

To obtain the value of k, substitute 220 for F, 40 for A and 5 for s in the equation (1).

220=k(40)(52)220=k(40)(25)220=k(1000)2201000=k

On further simplification,

k=22100k=1150k=0.22

That is, the value of k is 0.22.

Compute the speed of the boat with wetted surface area 28ft2 and drag force is 175lb as follows.

Substitute 28 for A, 175 for F and 0.22 for k in equation (1).

175=0.22(28)(s2)175=6.16(s2)1756.16=s228.41=s2

On further simplification,

28.409=s228.41=s5.33=s

Thus the speed of the boat is 5.33mi/h.

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