BuyFind

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 1, Problem 137RE
To determine

To calculate:The equation that depicts that the terminal velocity of parachutist v varies directly with respect to the square root of his weight w and use it to find out the terminal velocity when the parachutist weighs 240 lbs. if the 160 lbs. parachutist attains a terminal velocity of 9 miles per hour.

Expert Solution

Answer to Problem 137RE

The terminal velocity when the parachutist weighs 240 lbs. is v11.02 miles per hour.

Explanation of Solution

Given information:

Here, the terminal velocity of parachutist v varies directly with respect to the square root of his weight w

Also, 160 lbs. parachutist attains a terminal velocity of 9 miles per hour.

New weight is 240 lbs.

Formula used:

For 2 variables say, x and y , the statement x is directly proportional to y can be written as:

  xαy

Which can be written as:

  x=ky

Where k denotes the proportionality constant.

Similarly the statement x is inversely proportional to y can be interpreted as:

  xα1y

Which can be written as:

  x=k(1y)

Where k denotes the proportionality constant.

Calculation:

As the terminal velocity of parachutist v varies directly with respect to the square root of his weight w

For 2 variables say, x and y , the statement x is directly proportional to y can be written as:

  xαy

Which can be written as:

  x=ky

Where k denotes the proportionality constant.

Hence, this variation can be expressed as follows:

  vαw

  v=kw (1)

Where k denotes the proportionality constant.

It is also given v=9 miles per hour when w=160 lbs.

Put these values in (1) to get:

  9=k1609=k4*4*109=k410k=9410

Therefore, the proportionality constant k=9410

Therefore, (1) reduces to v=9410w

Now for new weight of w=240 lbs.

Replace the value of k=9410 and w=240 in (1) to get:

  v=9410240v=9410415v11.02

Thus, the terminal velocity when the parachutist weighs 240 lbs. is v11.02 miles per hour.

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