Word Problem (pre Calc)

Question

1. 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)=125-5t^2 .
2. Determine the average rate of change between the third and fourth second of the laptop’s flight.
3. Estimate the rate at which the laptop hits the ground.

Answer 1

a. Average rate of change is:r _av = [h(4) - h(3)]/(4 - 3) = [(125 - 5·4²) - (125 - 5·3²)]/1 = - 35 m/s

b. We can find time of motion from equation h(t) = 0, 125 - 5t² = 0, t² = 25, t = 5 s

Rate r(t) = d/dt(ht) = - 10t. Laptops hits the ground with rate r(5) = - 10·5 = - 50 m/s.

Minus means that vector of rate is looking down.