# The equation that depicts that the maximum range of the projectile R varies directly to square of its velocity v and use it to find out the maximum range if the ball is thrown at 70 miles per hour and if it is given thatthemaximum range of 242 feet is attained when ball is thrown with a velocity of 60 miles per hour.

### 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, Problem 138RE
To determine

## To calculate:The equation that depicts that the maximum range of the projectile R varies directly to square of its velocity v and use it to find out the maximum range if the ball is thrown at 70 miles per hour and if it is given thatthemaximum range of 242 feet is attained when ball is thrown with a velocity of 60 miles per hour.

Expert Solution

The maximum range if the ball is thrown at 70 miles per hour is R329.39 feet

### Explanation of Solution

Given information:

Here, the maximum range of the projectile R varies directly to square of its velocity v

Also, the maximum range of 242 feet is attained when ball is thrown with a velocity of 60 miles per hour.

New velocity is 70 miles per hour

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 maximum range of the projectile R varies directly to square of its velocity v

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:

Rαv2

R=kv2 (1)

Where k denotes the proportionality constant.

It is also given R=242 feet when v=60 miles per hour.

Put these values in (1) to get:

242=k(60)2k=2423600k=1211800

Therefore, the proportionality constant k=1211800

Therefore, (1) reduces to R=1211800v2

Now for new velocity of v=70 miles per hour.

Replace the value of k=1211800 and v=70 in (1) to get:

R=1211800(70)2R=1211800(4900)R329.39

Thus, the maximum range if the ball is thrown at 70 miles per hour is R329.39 feet

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