Question

The height of a model rocket in flight can be modelled by the equation

h(t)= -4.9 t²+25t+2,where h is the height in metres at t seconds.
Determine the average rate of change in the model rocket's height with the respect to time during.
a. the first second b.the second second

Answer 1

Average rate of change = 10.3 ft/sec.

Explanation:

The formula for the average rate of change is given by:

`AROC=(f(b)-f(a))/(b-a)`

Thus, we substitute 2 for b and 1 for a.

For the numerator, we substitute these values for t in h(t) and for the denominator, we simply subtract:

`AROC=([(-4.9(2)^2+25(2)+2)-(-4.9(1)^2+25(1)+2)])/((2-1))\\ \\AROC=((-4.9*4+50+2)-(-4.9+25+2))/(1) \\\\AROC={(-19.6+50+2)-(22.1)}{}\\ \\AROC= 32.4-22.1\\\\AROC=10.3`

Thus, the average rate of change in the model's rocket height in terms of time is 10.3 ft/sec.