Answer
a) $(t-1)(-4.9t+20.1)$
b) $20.1-4.9t$
c) $15.2$ m/s
Work Step by Step
a)
h(t) = $25-4.9t^{2}$
h(1) = $25(1)-4.9(1)^{2}$ = $20.1$
h(t) - h(1) = $25-4.9t^{2}-20.1$ = $(t-1)(-4.9t+20.1)$
b) interval [1, t]
average velocity = $\frac{h(t) -h(1)}{t-1}$ = $\frac{(t-1)(-4.9t+20.1)}{t-1}$ = $-4.9t+20.1$ = $20.1-4.9t$
c)
t =1.01
average velocity = $20.1-4.9(1.01)$ = $15.151$
t =1.001
average velocity = $20.1-4.9(1.001)$ = $15.1951$
t =1.0001
average velocity = $20.1-4.9(1.0001)$ = $15.19951$
t =1.00001
average velocity = $20.1-4.9(1.00001)$ = $15.199951$
The instantaneous velocity is approximately = 15.2 m/s
