Chapter 4, Problem 83GP

To determine

To find: The speed of a girl at the start of her coast.

Answer to Problem 83GP

A girl was moving with velocity 12.1 m/s.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Mass of ice skater, }m=65\text{ kg}\\ \text{Coefficient of kinetic friction, }{\mu }_k=0.10\\ \text{Distance covered by ice skater, }s=75\text{ m}\\ \text{Final velocity, }v=0\end{array}$

Formula Used:

  $\begin{array}{l}\text{Kinetic frictional force, }{f}_k={\mu }_{k}N\\ \text{Normal reaction, }N=mg\\ \text{Acceleration, }\\ a=\frac{-f_k}{m}\\ a=\frac{-{\mu }_{k}mg}{m}\\ a=-{\mu }_{k}g\\ v^2=u^2+2as,\\ v=\text{ Final velocity}\\ u=\text{ Initial velocity}\end{array}$

Calculation:

Substitute the values to find the acceleration.

  $\begin{array}{l}a=-{\mu }_{k}g\\ a=-0.10\times 9.8\\ a=-0.98{\text{ m/s}}^2\end{array}$

Substituting the values,

  $\begin{array}{l}{v}^2=u^2+2as\\ 0=u^2+2\times \left(-0.98\right)\times 75\\ u=\sqrt{147}\text{ m/s}\\ u=12.1\text{ m/s}\end{array}$

Conclusion:

Therefore, a girl was moving with velocity 12.1 m/s.