[SOLVED] Rates of Change Problem

**DaCoo911** · February 12th 2009, 01:01 PM

From a platform tower 10 m high, a diver performs a handstand dive.
His height, h, in metres above the water at t seconds can be modelled by
h(t) = 10 - 4.9t^2. Estimate the rate at which the diver enters the water.

The answer is supposed to be -14m/s i just don't understand how to get to that answer. At first a solution seemed simple, but i got the wrong answer.

Thanks in advanced, Joe

**Amanda H** · February 12th 2009, 03:02 PM

First find the time taken for the diver to fall. Find t when h=0:

$h(t) = 10 - 4.9t^2$
$0 = 10 - 4.9t^2$
$10 = 4.9t^2$
$t = \sqrt {\frac{10}{4.9}}$

to find the rate at which the diver enters the water (speed) differentiate:

$v(t) = -9.8t$

Then find the speed for the value of t found:

$v(t) = -9.8*\sqrt {\frac{10}{4.9}}$
$= -14m/s$

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