Question #17242

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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. use the notation v to denote h′: v=h′.

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. 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.

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. use the notation v to denote h′: v=h′.

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. 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.

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