Suppose you have a street light at a height H. You drop a rock vertically so that it hits the ground at a distance d from the street light. Denote the height of the rock by h. The shadow of the rock moves along the ground. Let s denote the distance of the shadow from the point where the rock impacts the ground. Of course, s and h are both functions of time.

Question

anonymous · Answer

To enter your answer into WeBWorK use the notation v to denote h′:

anonymous · Answer

a) Then the speed of the shadow at any time while the rock is in the air is given by s′=_________ (where s′ is an expression depending on h, s, H, and v (You will find that d drops out of your calculation.) Now consider the time at which the rock hits the ground.

anonymous · Answer

b) At that time h = s = 0 The speed of the shadow at that time is s′=_____________________ where your answer is an expression depending on H, v, and d. Hint: Use similar triangles and implicit differentiation. For the second part of the problem you will need to compute a limit. Here is the diagram: https://webwork.elearning.ubc.ca/webwork2_files/tmp/MATH104-184-ALL_2013W1/img/f16baefb-f23b-3d46-a94e-245cb0a338ff___d7a88d53-941e-319a-8956-39f9ab6d859b.gif

goformit100 · Answer

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