Question

You throw a $5.5$g coin straight down at $4.0$m/s from a $35$-m-high bridge.

a. How much work does gravity do as the coin falls to the water below? b. What is the speed of the coin just as it hits the water?

Short answer

a). $1.89$J work does gravity do as the coin falls to the water below

b). The speed of the coin is$26.49$m/s

Step-by-step solution

Step 1. Given Information

Mass od the coin $=5.5g=0.0055Kg$

Speed of the coin $v_i=4$m/s

Height of the bridge$s=35$m

Step 2. Part a). The work done by the gravity force

As the coin fall downward it accelerates with $g$as a result its velocity changes,

Hence by calculating a change in its kinetic energy in the duration till it hits the water surface,

localid="1648137947470" $$\begin{gathered} W=\left(\overrightarrow{F_G}·\overrightarrow{∆r}\right)J \\ W=\left(F_G∆r\cos 0°\right)J \\ W=\left(0.0055\times 9.8\times 35\right)J \\ W=\left(1.89\right)J \end{gathered}$$

Step 3. Part b). Find its velocity before hitting water

Now,

For the equation of the motion:

$$\begin{gathered} {v_f}^2=\left({v_i}^2+2as\right)m/s \\ =\left(4^2+2\times 9.8\times 35\right)m/s \\ =\left(702\right)m/s \\ {v}_f=\left(26.49\right)m/s \end{gathered}$$