Answer to Question #195400 in Calculus for Angela Artita

Question #195400

Shan, who is 2 meters tall, is approaching a post that holds a lamp 6 meters above the ground. If he is walking at a speed of 1:5 m/s, how fast is the end of his shadow moving (with respect to the lamp post) when he is 6 meters away from the base of the lamp post? 


1
Expert's answer
2021-05-20T07:56:02-0400

equation of a straight line with the end of the shadow from time to time. we know that it passes through two points depending on time. the first point is (6-"\\frac{t}{5}" , 2). Second (0, 6)."y=k(t)x+b(t).\nx=0,y=6\\implies b(t)=6\\\\\nx=6-\\frac{t}{5},y=2=> 2=k(6-\\frac{t}{5})+6;k=\\frac{-4}{6-\\frac{t}{5}}\\\\\ny=0,0=k(t)x+b(t),x=-6*\\frac{6-\\frac{t}{5}}{-4}=9-\\frac{3t}{10}\\\\\n|x'(0)|=0.3"

Answer:0.3


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