(a) To compute the angle ∠ A .

Question

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?

Answer 1

Question

Chapter 78, Problem 16A

To determine

(a)

To compute the angle ∠A.

To determine

(b)

To compute the angle ∠T.

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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?

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