Solve the problem.
-A $53 \mathrm {~m}$-long steel beam is anchored at one end to a piling $7 \mathrm {~m}$ above the ground. Assume that when a certain heavy object is placed $\mathrm { d }$ meters from the anchored end, the beam bends s meters where
$$s = \left( 3 \times 10 ^ { - 6 } \right) d ^ { 2 } ( 150 - d ) \text {. }$$
How far is the heavy object from the anchored end if the vertical deflection is $0.50 \mathrm {~m}$ ? (Round to the nearest hundred)
A) $141.70 \mathrm {~m}$
B) $38.70 \mathrm {~m}$
C) $30.40 \mathrm {~m}$
D) $27.50 \mathrm {~m}$

Question

Quizplus · Accepted Answer

To solve for $d$ when $s = 0.50$, substitute $s = 0.50$ into the equation and solve for $d$:$$0.50 = (3 \times 10^{-6})d^2(150 - d).$$This is a cubic equation in terms of $d$. Solving this equation (typically requiring numerical methods or a graphing approach due to its complexity), we find that $d \approx 38.70 \mathrm{~m}$, which is the distance from the anchored end to where the heavy object is placed to cause a 0.50 m vertical deflection.

Solve the Problem 53 m53 \mathrm {~m}53 m -Long Steel Beam Is Anchored at One End to a Is

Solve the Problem $53 \mathrm {~m}$ -Long Steel Beam Is Anchored at One End to a Is