A ladder 5m long is leaning …
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Anwesha Mishra 7 years, 11 months ago
Then, by Pythagoras theorem, we have:
x2 + y2 = 25 [Length of the ladder = 5 m]
⇒y=25−x2−−−−−−√
Then, the rate of change of height (y) with respect to time (t) is given by,
dydx=−x25−x2−−−−−−√.dxdt
It is given that
dxdt=2cm/s.
∴dydt=−2x25−x2−−−−−−√
Now, when x = 4 m, we have:
∴dydt=−2×425−42−−−−−−√=−83
Hence, the height of the ladder on the wall is decreasing at the rate of
83
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