An irrigation drip arm is 28 feet long and pivots about a center one revolution each hour. A “drip hole” H is located 28 feet from the pivot point.

(a) What is the linear speed of H in units of feet/hour ,feet/minute ,feet/second , and inches/second .
(b) What is the required drip rate (in drips second ) if we
want at least 4 drips for every 1 inch H travels. (The drip rate must be a counting number; i.e. 1,2,3,4,...)
(c) Suppose 10 drips = 1 cc (cubic centimeter).
How many liters flow from H after 25 minutes, assuming the drip rate computed in b.? (1 liter = 1, 000 cc)
(d) How much water flows from H after the arm has made 3 complete revolutions (assuming the drip rate computed in b.)?

(a) To find the linear speed of the drip hole H, we need to determine the distance it travels in one hour. Since the irrigation drip arm has a length of 28 feet and completes one revolution in one hour, the circumference of the circular path it traces is equal to the length of the arm.

The formula for the circumference of a circle is C = 2πr, where r is the radius. In this case, the length of the arm is the diameter (2r), so the radius is half the length of the arm: r = 28 feet / 2 = 14 feet.

Using the circumference formula, the distance traveled by the drip hole H in one hour is C = 2π(14) = 28π feet.

To convert the linear speed from feet per hour to other units:
- Feet per minute: Divide the distance in feet per hour by the number of minutes in an hour (60 minutes).
- Feet per second: Divide the distance in feet per hour by the number of seconds in an hour (3,600 seconds).
- Inches per second: Multiply the distance in feet per second by the number of inches in a foot (12 inches).

So, the linear speed of H is:
- Feet/hour: 28π feet/hour
- Feet/minute: (28π feet/hour) / (60 minutes/hour)
- Feet/second: (28π feet/hour) / (3600 seconds/hour)
- Inches/second: [(28π feet/hour) / (3600 seconds/hour)] * (12 inches/foot)

(b) To determine the required drip rate, we need to calculate the number of drips for every inch H travels. We know that for every 4 drips, H travels 1 inch. Therefore, the drip rate will be the reciprocal of this ratio.

Drip rate = 1 / (1 inch / 4 drips) = 4 drips/inch

(c) To find the amount of water flowing from H after 25 minutes, assuming the drip rate computed in part (b), we need to calculate the total number of drips in 25 minutes.

Number of drips = Drip rate × Time in minutes = 4 drips/inch × 25 minutes

Now, since 10 drips equal 1 cc, we can determine the number of cubic centimeters (cc) flowing from H:

Number of cc = Number of drips / 10 = (4 drips/inch × 25 minutes) / 10 = 10 cc

Finally, to convert cubic centimeters (cc) to liters, we divide by 1000 (since 1 liter equals 1000 cc):

Number of liters = Number of cc / 1000 = 10 cc / 1000 = 0.01 liters

Therefore, after 25 minutes, assuming the drip rate computed in part (b), 0.01 liters will flow from H.

(d) To find the amount of water flowing from H after the arm has made 3 complete revolutions, we need to calculate the total number of drips.

Each revolution of the arm is equivalent to one complete circle, and we know that the circumference of the circle is 28π feet. Therefore, the distance traveled by the drip hole H in three revolutions is:

Total distance = 3 revolutions × 28π feet/revolution = 84π feet

Using the drip rate computed in part (b), we can calculate the total number of drips:

Number of drips = Drip rate × Total distance = 4 drips/inch × (84π feet)

As we don't have the exact value of π, we can leave the answer in terms of π or use an approximation (e.g., 3.14) to calculate the numerical value.

Note: If you would like the numerical value, please let me know the approximation of π you would like to use.