A frustrated office worker throws his laptop out of his business’s high-rise

office building. The height, h, in meters of the laptop above the ground at t
seconds can be modelled by
h(t)=125=125-5t^2
Estimate the instantaneous rate at which the laptop hits the ground.

Where is there a high-rise with windows that open?

Anyway -- Graham has just answered your question.

http://www.jiskha.com/display.cgi?id=1374270782

To estimate the instantaneous rate at which the laptop hits the ground, we need to calculate the derivative of the given function h(t). The derivative represents the rate of change of the function with respect to time.

In this case, the given function is h(t) = 125 - 5t^2.

To find the derivative, we need to differentiate each term of the function with respect to t. The derivative of a constant term (125 in this case) is zero. The derivative of 5t^2 can be found using the power rule of differentiation.

The power rule states that if we have a term of the form x^n, the derivative is nx^(n-1).

Applying the power rule to the function h(t) = 125 - 5t^2, we get:

h'(t) = 0 - (10t)

Simplifying further, we have:

h'(t) = -10t

The instantaneous rate at which the laptop hits the ground is given by h'(t). However, the question asks for the estimate of this rate when the laptop hits the ground. Therefore, we need to find the value of t when h(t) is equal to zero (ground level).

Setting h(t) = 0:

0 = 125 - 5t^2

Rearranging the equation, we have:

5t^2 = 125

Dividing both sides by 5, we get:

t^2 = 25

Taking the square root of both sides, we find:

t = ±5

Since we are interested in the time when the laptop hits the ground, t = -5 can be disregarded, as time cannot be negative in this context. Therefore, the estimated time at which the laptop hits the ground is t = 5 seconds.

Substituting this value back into the derivative function h'(t) = -10t, we can find the estimated instantaneous rate at which the laptop hits the ground:

h'(5) = -10 * 5 = -50 m/s

Therefore, the estimated instantaneous rate at which the laptop hits the ground is -50 m/s.