Question

Ken is 6 feet tall and is walking away from a streetlight. The streetlight has its light bulb 14 feet above the ground, and Ken is walking at the rate of 1.7 feet per second. Find a function, d(t), which gives the distance Ken is from the streetlight in terms of time. Find a function, , which gives the length of Ken's shadow in terms of d. Then find .

Answer 1

Ken's distance is:  d(t)=1.7t

Ken's shadow is:

(14-6)/d(t)=14/s

8/d(t)=14/s

s=14d(t)/8

s=1.75d(t) and using the value for d(t) we have:

s=1.75(1.7t)

s=2.975t  and if you want it in terms of d, d=1.7t, t=d/1.7 so

s=2.975(d/1.7)

s=1.75d