Question

2 a crane at a construction site lowers a steel beam into position at a rate of $2\frac{1}{2}$ feet per second. what is the change in the height of the steel beam after 14 seconds? \\(\boldsymbol{\text{a}}\\) \\(-35\\) feet \\(\boldsymbol{\text{b}}\\) \\(-28\frac{1}{2}\\) feet \\(\boldsymbol{\text{c}}\\) \\(28\frac{1}{2}\\) feet \\(\boldsymbol{\text{d}}\\) \\(35\\) feet

Explanation:

Step1: Convert mixed number to improper fraction

The rate is \( 2\frac{1}{2} \) feet per second. Convert \( 2\frac{1}{2} \) to an improper fraction: \( 2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2} \) feet per second. Since the beam is being lowered, the rate is negative, so the rate \( r=-\frac{5}{2} \) feet per second.

Step2: Use the formula for distance (change in height)

The formula for distance (or change in height, \( \Delta h \)) is \( \Delta h=r\times t \), where \( r \) is the rate and \( t \) is the time. Here, \( t = 14 \) seconds. Substitute \( r=-\frac{5}{2} \) and \( t = 14 \) into the formula: \( \Delta h=-\frac{5}{2}\times14 \).

Step3: Calculate the product

Simplify \( -\frac{5}{2}\times14 \). \( 14\div2 = 7 \), so \( -\frac{5}{2}\times14=-5\times7=-35 \) feet.

Answer:

A. -35 feet