A tight rope is attached 30 ft above the ground between buildings A and B, which are 50 ft apart. A guy is walking on the rope at a constant rate of 2 ft/s, and is illuminated by a spotlight (S) 70 ft above on building A

....S_______50_________

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..A|__________________|B <tightrope

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.30|.............................|

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1. How fast is the shadow of the tightrope walker's feet moving along the ground when he is midway between the buildings?

I got 20/7 ft/s. I used similar triangles and didnt even have an X in the deriv (just x') so the rate would always be the same no matter where the guy is on the rope....is that right?

2. How far from point A is he when the shadow of his feet reaches the base of B building?

I got 35 feet, using similar triangles

3. How fast is the shadow of the tightrope walker's feet moving up the wall of the B building when he is 10 feet from point B?

I got 4.375 ft/s

am i right?

and another: Car B is 30 miles directly east of Car A and begins moving west at 90 mph. At the same time, car A begins movie north at 60 mph.

a. after 1/10 of an hour has elapsed, at what rate are the cars getting closer together.

used distance formula and got 277.4033 mph. (that doesnt seem right)

b. what will be the minimum distance between the cars, and at what time t does the minimum distance occur