# Calculus UNIT304 What about parametrics?

## 2795 days ago by MATH4R2013

#1a) you are falling down a 1600ft well, f(t)=-16*t^2 f(t)=-16*t^2 g(t)=diff(f(t),t) show(f(t)) show(g(t)) #1b) How long before you hit bottom? How fast are you going then? show(solve(f(t)==-1600,t)) show(g(10))
 \newcommand{\Bold}{\mathbf{#1}}-16 \, t^{2} \newcommand{\Bold}{\mathbf{#1}}-32 \, t \newcommand{\Bold}{\mathbf{#1}}\left[t = \left(-10\right), t = 10\right] \newcommand{\Bold}{\mathbf{#1}}-320
#2a) you shoot a cannon ball straight up, f(t)=160*t-16*t^2 f(t)=160*t-16*t^2 g(t)=diff(f(t),t) show(f(t)) show(g(t)) #2b) How long before it starts falling? How high is the zenith? show(solve(g(t)==0,t)) show(f(5)) #2c) When is the cannon ball 256 ft high? How fast is it going then? show(solve(f(t)==256,t)) show(g(2)) show(g(8))
 \newcommand{\Bold}{\mathbf{#1}}-16 \, t^{2} + 160 \, t \newcommand{\Bold}{\mathbf{#1}}-32 \, t + 160 \newcommand{\Bold}{\mathbf{#1}}\left[t = 5\right] \newcommand{\Bold}{\mathbf{#1}}400 \newcommand{\Bold}{\mathbf{#1}}\left[t = 2, t = 8\right] \newcommand{\Bold}{\mathbf{#1}}96 \newcommand{\Bold}{\mathbf{#1}}-96
#3a) 83AB3a x(t)=t^3-6*t^2+9*t+11, find x'(0) f(t)=t^3-6*t^2+9*t+11 g(t)=diff(f(t),t) show(f(t)) show(g(t)) show(g(0)) #3b) 83AB3b x(t)=t^3-6*t^2+9*t+11, when is the object moving to the left? show(solve(g(t)==0,t)) show(plot(g(t),0,5))
 \newcommand{\Bold}{\mathbf{#1}}t^{3} - 6 \, t^{2} + 9 \, t + 11 \newcommand{\Bold}{\mathbf{#1}}3 \, t^{2} - 12 \, t + 9 \newcommand{\Bold}{\mathbf{#1}}9 \newcommand{\Bold}{\mathbf{#1}}\left[t = 3, t = 1\right]  