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A swimmer runs over a horizontal diving board at a speed of 0.95 meters/second. 2.0 seconds after she dives, she hits the water. What was the height of the diving board from the water's surface and how far from the board was the swimmer when she hit the water?
A. 20 meters, 1.9 meters
B. 1.9 meters, 20 meters
C. 20 meters, 2.0 meters
D. 2.2 meters, 20 meters

Respuesta :

sqdancefan

Answer:

  A.  20 meters, 1.9 meters

Explanation:

The diver's horizontal speed is 0.95 m/s, so in 2 seconds, she travels ...

  distance = speed × time

  = (0.95 m/s)×(2 s) = 1.90 m

This is sufficient to point you to answer choice A.

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The usual formula for vertical motion under the influence of gravity is ...

  h(t) = -4.9t² +v0·t +h0

where v0 and h0 are the initial vertical speed and height, respectively. If there is no vertical speed to begin with, and the ending height is 0, then after 2 seconds, we have ...

  0 = -4.9·2² +h0

  19.6 = h0 . . . . . the starting height is 19.6 meters

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To simplify the numbers, the above formula is sometimes written ...

  h(t) = -5t² +h0

Using this formula, we get h0 = 20 meters, matching choice A.

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