Answer to Question #175427 in Calculus for kienth bryan doroin

Question

starting from the same point, Biden starts walking eastward at 52 m/s while Trump starts running towards the south at 86 m/s. How fast is the distance between Biden and Trump increasing after 2 seconds? (Input your final answer on the box below without units of measure

Answer 1

In 2secs Biden would have covered 104m

While Trump would have covered 172m

Using Pythagoras theorem

$x^2+y^2=z^2$

x=104 y=172 while z is the distance between them

$z=\sqrt{104^2+172^2}=201m$

differentiating the Pythagoras theorem we have $2x{dx \over dt} + 2y{dy \over dt}=2z{dz \over dt}$

${dx \over dt}= 52m/s$ ${dy \over dt}=86m/s$ ${dx \over dt}= ?$

$2(104)(52) +2(172)(86)=2(201){dx \over dt}$

${dz \over dt}=100.5m/s$