# Calculus UNIT502A: What are Related Rates?

## 2756 days ago by MATH4R2013

#29 p256: A man 6' tall walks toward a lamp post 16' tall #29 p256: at a rate of 5 ft/s. How fast is his shadow changing? var('y') show(solve(16/6==(x+y)/x,x)) xp=3*(-5)/5 show(xp) #xp=-3 ft/s
 \newcommand{\Bold}{\mathbf{#1}}\left[x = \frac{3}{5} \, y\right] \newcommand{\Bold}{\mathbf{#1}}-3
#13 p256: A plane, 7 miles in the air flies over a radar antenna. #13 p256: The moment that the plane is 10 miles from the radar, #13 p256: the distance from the radar to the plane is changing #13 p256: at a rate of 300 mi/hr. How fast is the plane flying horizontally? var('z,zp,xp') show(z^2==x^2+49) show(2*z*zp==2*x*xp) show(2*10*300==2*sqrt(51)*xp) show(solve(2*10*300==2*sqrt(51)*xp,xp).rhs().n()) #xp is about 420.084 mi/hr
 \newcommand{\Bold}{\mathbf{#1}}z^{2} = x^{2} + 49 \newcommand{\Bold}{\mathbf{#1}}2 \, z \mbox{zp} = 2 \, x \mbox{xp} \newcommand{\Bold}{\mathbf{#1}}6000 = 2 \, \sqrt{51} \mbox{xp} \newcommand{\Bold}{\mathbf{#1}}420.084025208403