Asked by Sandra
A light hangs 15 ft. directly above a straight walk on which a man 6 ft. tall is walking. How fast is the end of the man's shadow travelling when he is walking away from the light at a rate of 3 miles per hour?
Answers
Answered by
Reiny
did you make your sketch ??
let the length of the man's shadow be x ft
let the distance he is from the lightpost be y
by ratios:
6/x = 15(x+y)
6x + 6y = 15x
6y = 9x
2y = 3x
2dy/dt = 3dx/dt
but dy/dt = 3
so 6 = 3 dx/dt
dx/dt = 2
His shadow is lengthening at 2 ft/s
but he is also moving at 3 ft/s
so d(x+y)/dt = 5 ft/s
In this kind of question we have to be careful what is asked:
at what rate is the shadow increasing ---- 2 ft/s
at what rate is the shadow moving ----- 5 ft/s
an analogy would be a man walking in a car of a moving train:
if the man is walking in the car at 3 ft/s
but the train is moving at 50 ft/s, to an observer looking in would see the man moving at 53 ft/s
let the length of the man's shadow be x ft
let the distance he is from the lightpost be y
by ratios:
6/x = 15(x+y)
6x + 6y = 15x
6y = 9x
2y = 3x
2dy/dt = 3dx/dt
but dy/dt = 3
so 6 = 3 dx/dt
dx/dt = 2
His shadow is lengthening at 2 ft/s
but he is also moving at 3 ft/s
so d(x+y)/dt = 5 ft/s
In this kind of question we have to be careful what is asked:
at what rate is the shadow increasing ---- 2 ft/s
at what rate is the shadow moving ----- 5 ft/s
an analogy would be a man walking in a car of a moving train:
if the man is walking in the car at 3 ft/s
but the train is moving at 50 ft/s, to an observer looking in would see the man moving at 53 ft/s
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.