Motion System Design
Fun with Fundamentals: Problem 212

Fun with Fundamentals: Problem 212

Timber tantrum

Problem 211 — The shadow knows, as this month’s problem by Larry Little of Springfield, Mo., demonstrates.

“You break-a my house, I break-a you face!” shouted Rufus McTwipp.

“It’s not a problem,” retorted Jeremiah Jubb. “The tree we’re going to cut down is far enough away from your home.”

The house was 220 ft from the tree. At noon, McTwipp noticed the tree’s shadow was directly underneath the tree. At one o’clock the shadow was 53.5 ft long. Compute the height of the tree to see if Jubb will need plastic surgery.

Technical consultant, Jack Couillard, Menasha, Wis.

Solution to last month’s problem 210 — You have your ups and downs if you answered yes. Here’s the angle:

g = Gravitational constant, 32.2 ft/sec2
t1= Time it takes the ball to reach its zenith, sec
t2 = Time it takes ball to reach the tree, sec
v0 = Initial velocity of ball, given as 120 fps
x = Horizontal distance traveled by the ball, ft
y = The height of the ball during its flight, ft

We must see whether the ball clears the 55-ft pine tree. First compute the time it takes the ball to reach the tree. It is stated in the problem that the tree is midway between Puff and the 18th hole. It is therefore 65 yds or 195 ft. from Puff.

The height of the ball at t2 is:

The ball clears the tree by 0.9 ft. To find out whether it makes the green, solve for the distance. First find the time it takes the ball to reach its zenith:

Since Puff was 390 ft away from the hole when he made the shot, it landed on the green.

Congratulations to Bob Pauplis of Andover, Mass., who won our September contest by having name drawn from the 105 correct responses out of a total of 118 contestants. A pack of Nerd Kards is in the mail to him.

Nerd Kards, which are the same size as baseball cards, describe the great scientists and mathematicians from ancient times down through the twentieth century. Each of the 100 Kards contains a photo or drawing of the individual and a description of his career and achievements. Many are Nobel Prize winners.

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Fun with Fundamentals: Problem 212

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