Question

Jack and Jill take 14 minutes to fetch a pail of water by walking 340 m [W], then 129 m [S].Calculate :a. Their total displacementb. Their average speedc. Their average velocity

Answer 1

The displacement refers to a change in the position. We know they walk 340 m to the West and 129 meters to the South. Let's draw the vectors. Also, the displacement is a vector.

To find the total displacement, we have to add the vectors. We'll use i for horizontal components and j for vertical components.

(a) The total displacement is

`\vec{R}=(-340i-129j)m`

The average speed refers to the quotient between the total distance traveled and the time elapsed.

`\bar{v}=(d_(total))/(t_(total))=(340m+129m)/(14\min )`

But, transform 14 minutes to seconds. Just multiply 14*60.

`\bar{v}=(469m)/(14\cdot60\sec)=(469m)/(840\sec )\approx0.56((m)/(s))`

(b) Their average speed is 0.56 (m/s).

At last, the average velocity refers to the total displacement divided by the time elapsed.

`\begin{gathered} \vec{v}=\frac{\vec{R}}{t}=((-340i-129j)m)/(840\sec )=(-(340i)/(840)-(129j)/(840))((m)/(s)) \\ \vec{v}=(-0.40i-0.15j)((m)/(s)) \end{gathered}`

(c) Their average velocity is (-0.40i-0.15j)(m/s)