Thread: Shadows and distance, I need a formula to solve for Object 2

Looking for a formula to solve this word problem. Please Help

A shadow from object 1 projects on a wall 1.75 X larger than its original size. Object 1 is 4.5 ft from the wall the shadow has been casted on. Object 2 has a known size which cast a shadow of 1.25 X its original size. How far is object 2 from the wall.

Originally Posted by crah28

Looking for a formula to solve this word problem. Please Help

A shadow from object 1 projects on a wall 1.75 X larger than its original size. Object 1 is 4.5 ft from the wall the shadow has been casted on. Object 2 has a known size which cast a shadow of 1.25 X its original size. How far is object 2 from the wall.

Let :

$\displaystyle r_1=1.75~ , r_2=1.25~ ,x_1=4.5 ~ , x_2 = ?$

and denote distance of the source of the light from the wall as d . Therefore :

$\displaystyle d=r_1(d-x_1) \Rightarrow d=1.75(d-4.5) \Rightarrow d=10.5$

Hence :

$\displaystyle d=r_2(d-x_2) \Rightarrow x_2=\frac{dr_2-d}{r_2} \Rightarrow x_2=2.1$

Thanks for your help, the formula was spot on.