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Problem 1236

Find the height of a tree which casts a shadow 20 feet long at the same time a vertical yard stick casts a shadow 30 inches long.

Expert verified

The height of the tree is 24 feet, which we found by setting up a proportion using the given shadow lengths and solving for the unknown height, \(h\).

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Chapter 44

On a map, \(3 / 16 \mathrm{pr}\) inch represents 10 miles. What would be the length of a line on the map which represents 96 miles?

Chapter 44

The weight \(\mathrm{W}\) of an object above the earth varies inversely as the square of the distance \(\mathrm{d}\) from the center of the earth. If a man weighs 180 pounds on the surface of the earth, what would his weight be at an altitude of 1000 miles? Assume the radius of the earth to be 4000 miles.

Chapter 44

The area of a sphere is directly proportional to the square of the radius. If a sphere of radius 3 inches has an area of \(36 \pi\) square inches, deduce the formula for the area of a sphere.

Chapter 44

Solve the proportion \((\mathrm{x}+1) / 4=15 / 12\)

Chapter 44

A falling body strikes the ground with a velocity \(\mathrm{v}\) which varies directly as the square root of the distance s it falls. If a body that falls 100 feet strikes the ground with a velocity of 80 feet per second, with what velocity will a ball dropped from the Washington monument (approximately 550 feet high) strike the ground?

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