Distance to the Horizon The distance that a p...

Question

Distance to the Horizon The distance that a person can see to the horizon on a clear day from a point above the surface of Earth varies directly as the square root of the height at that point. If a person 144 m above the surface of Earth can see 18 km to the horizon, how far can a person see to the horizon from a point 64 m above the surface?

Accepted Answer

Using variation techniques solve the following problem. A particle's root means square velocity is directly proportional to the square root of its temperature. In Kelvin, if an oxygen gas particle has a velocity of 490 m per second at 292 in Kelvin find this velocity at 338 k. Then we have four possible answers 5 67. 27.18 7 56.20 and 25.20 all in meters per second. Now the problem tells us the root means square velocity is directly proportional to the square root of a symmetry in Kelvin. That just means an increase and root mean square velocity corresponds with an increase in the square root of temperature of Kelvin. In other words, we can write this function as V R MS equals the square root of Kelvin T K. Like so now with variation, we're going to multiply one of these by a constant of proportionality to just get a general constant a transfer between units, let's say multiply R squared of T K by K. Then we can solve for Kate. So it tells us our velocity is 490 m per second equals K multiplied by the square root temperature in Kelvin to 92. Calvin Mike said now we can actually simplify our square root up to a 92. We would get 4 90 meres per second plus K multiplied five square of four multiplied by 73. Or in other words, this simplifies to two square roots of K Raced to the one half power. No, we can divide both sides by two square roots of 73 to get K by itself. When we do that, we get 2 45 divided by the square of meters per second. Kelvin raced to the one half in units that equals K. Now we can find our new root means square velocity B R MS, I'll call this number two equals R K 2 45 divided by its squared of meters per second, multiplied by Kelvin raced to the one half, all this multiplied by the square root of our new temperature. 338 Kelvin. We can now multiply all of our numbers and simplify when we do that, hit our second V R S as equals to about 5 27.18 m per second. This means the answer to our problem is answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Key Concepts

Direct Variation

Square Root Function

Solving Proportions

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