1. a worker accidentally drops a tool from a scaffold 20m above the ground.\na. how long does it take for…

Explanation:

Step1: Use free - fall displacement formula

The vertical displacement formula for free - fall is $y = y_0+v_0t-\frac{1}{2}gt^2$, where $y = 0$ (ground level), $y_0=20m$ (initial height), $v_0 = 0m/s$ (released from rest), and $g = 9.8m/s^2$. So, $0 = 20+0\times t-\frac{1}{2}\times9.8t^2$.

Step2: Solve for time $t$

Rearranging the equation $4.9t^2=20$, we get $t=\sqrt{\frac{20}{4.9}}\approx2.02s$.

Step3: Use velocity - time formula for free - fall

The velocity - time formula is $v = v_0 - gt$. Since $v_0 = 0m/s$, then $v=-gt$. Substituting $t = 2.02s$ and $g = 9.8m/s^2$, we have $v=-9.8\times2.02\approx - 19.8m/s$. The negative sign indicates the direction is downward.

Step4: Suggest safety measures

Install safety nets below the scaffold to catch falling objects. Workers should also secure tools with lanyards to prevent accidental drops.

Answer:

a. Approximately $2.02s$ b. Approximately $- 19.8m/s$ c. Install safety nets and use tool lanyards.