SOLUTION: A light shines toward the ground from the top of a building wall that is 40 ft high. A kid in a tree house that is 25ft to the right of the building drops an apple from the same h

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A light shines toward the ground from the top of a building wall that is 40 ft high. A kid in a tree house that is 25ft to the right of the building drops an apple from the same h      Log On


   

Question 1153645: A light shines toward the ground from the top of a building wall that is 40 ft
high. A kid in a tree house that is 25ft to the right of the building drops an apple from the same height (40 ft). How fast is the shadow of the apple moving along the ground ½ sec later? Assume the apple falls at a distance 𝑠 = 16𝑡^2 in t seconds.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
first draw it:


given:
a building wall that is 40ft high
a tree house that is 25ft to the right of the building
the shadow of the apple moving along the ground 1%2F2 sec later
s=16%F0%9D%91%A1%5E2 in t seconds
two right triangles are similar, means corresponding sides are proportional
so,
x%2F%28x-24%29=40%2F%2840-s%29
x%2840-s%29=40%28x-24%29
cross%2840x%29-xs=cross%2840x%29-960
-xs=-960....multiply by -1
xs=960
x=960%2Fs
Differentiating with respect to t we have
dx%2Fdt=-%28960%2Fs%5E2%29%28ds%2Fdt%29

We are given s=16t%5E2⇒ ds%2Fdt+=+32t
At t+=+1%2F2, s+=+16%281%2F2%29%5E2=16%2F4+=+4 and ds%2Fdt+=+32%2F2+=+16.

Plugging these in we have
dx%2Fdt=-%28960%2F4%5E2%29%2816%29%28ft%2Fs%29=-960%28ft%2Fs%29