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Jo drops a marble from her apartment window, 20 meters above the ground. At the s ame height bu' 12 meters away, Doe watches the marble fall. When the height of the marble above the ground is h let 0 be the angle between L and M, where L is the horizontal line joining Jo and Doe, and where M represents Doe's line of sight to the marble. (a) Draw a picture of the scene, including L, M, and 0. Put the horizontal axis at ground level and indicate the position of the marble h(t) meters above ground level at time t. (b) Find 0 in terms of h, and then calculate de/dh. (c) Assume that h(t) = 20– 4.9t² until the marble hits the ground. Find d0/dt. Show geometrically why de /dt > 0, and then tell why the formula for de/dt tells us that in fact de/dt > 0. Note: It turns out that there is a value to for which de/dt has a maximum value. For 0(to) the marble appears to be falling the fastest. Can you find the value of to?

Jo drops a marble from her apartment window, 20 meters above the ground. At the s ame height bu' 12 meters away, Doe watches the marble fall. When the height of the marble above the ground is h let 0 be the angle between L and M, where L is the horizontal line joining Jo and Doe, and where M represents Doe's line of sight to the marble. (a) Draw a picture of the scene, including L, M, and 0. Put the horizontal axis at ground level and indicate the position of the marble h(t) meters above ground level at time t. (b) Find 0 in terms of h, and then calculate de/dh. (c) Assume that h(t) = 20– 4.9t² until the marble hits the ground. Find d0/dt. Show geometrically why de /dt > 0, and then tell why the formula for de/dt tells us that in fact de/dt > 0. Note: It turns out that there is a value to for which de/dt has a maximum value. For 0(to) the marble appears to be falling the fastest. Can you find the value of to?

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter10: Analytic Geometry
Section10.CT: Test
Problem 1CT
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Jo drops a marble from her apartment window, 20 meters above the ground. At the same height but 12 meters away, Doe watches the marble fall. When the height of the marble above the ground is h, let 0 be the angle between L and M, where L is the horizontal line joining Jo and Doe, and where M represents Doe's line of sight to the marble. (a) Draw a picture of the scene, including L, M, and 0. Put the horizontal axis at ground level, and indicate the position of the marble h(t) meters above ground level at time t. (b) Find 0 in terms of h, and then calculate d0/dh. (c) Assume that h(t) = 20– 4.9t² until the marble hits the ground. Find de/dt. Show geometrically why de/dt > 0, and then tell why the formula for de/dt tells us that in fact d0/dt > 0. Note: It turns out that there is a value to for which de/dt has a maximum value. For 0(to) the marble appears to be falling the fastest. Can you find the value of to?
Transcribed Image Text:Jo drops a marble from her apartment window, 20 meters above the ground. At the same height but 12 meters away, Doe watches the marble fall. When the height of the marble above the ground is h, let 0 be the angle between L and M, where L is the horizontal line joining Jo and Doe, and where M represents Doe's line of sight to the marble. (a) Draw a picture of the scene, including L, M, and 0. Put the horizontal axis at ground level, and indicate the position of the marble h(t) meters above ground level at time t. (b) Find 0 in terms of h, and then calculate d0/dh. (c) Assume that h(t) = 20– 4.9t² until the marble hits the ground. Find de/dt. Show geometrically why de/dt > 0, and then tell why the formula for de/dt tells us that in fact d0/dt > 0. Note: It turns out that there is a value to for which de/dt has a maximum value. For 0(to) the marble appears to be falling the fastest. Can you find the value of to?
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