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motikmotik
3 years ago
11

A 10-foot ladder is leaning straight up against a wall when a person begins pulling the base of the ladder away from the wall at

the rate of 1 foot per second. Calculate the true distance between the top of the ladder and the ground when the base of the ladder is 9 feet from the wall.
Physics
1 answer:
docker41 [41]3 years ago
8 0

Answer:

y = 4.36

Explanation:

Let the height of the ladder be L

L = 10

Also:

  • Let x = distance\ from\ the\ base\ of\ the\ ladder
  • Let y = height\ of\ the\ base\ of\ the\ ladder

When the ladder leans against the wall, it forms a triangle and the length of the ladder forms the hypotenuse.

So, we have:

L^2 = x^2 + y^2 --- Pythagoras Theorem

When the base is 9ft from the wall, this means that:

x = 9

Substitute 9 for x and 10 for L in L^2 = x^2 + y^2

10^2 = 9^2 + y^2

100 = 81 + y^2

Make y^2 the subject

y^2 = 100 - 81

y^2 = 19

Make y the subject

y = \sqrt{19

y = 4.36

<em>Hence, the true distance at that point is approximately 4.36ft</em>

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