Question

1. a worker accidentally drops a tool from a scaffold 20m above the ground.

a. how long does it take for the tool to hit the ground?
b. what is the tool’s velocity upon impact?
c. what kind of safety measures should be in place to prevent accidents like this?

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.