Chapter 4, Problem 73GP

To determine

Whether the cyclist will emerge from muddy stretch and the speed of the cyclist on emerging from muddy stretch.

Answer to Problem 73GP

The cyclist will emerge from muddy stretch with acceleration $-5.88\text{m}/{\text{s}}^2$ and the speed of the cyclist at the emerge from the muddy stretch is $3.83\text{m}/\text{s}$ .

Explanation of Solution

Given info:

The initial speed of the cyclist is, $u=12\text{m}/\text{s}$ .

The effective coefficient of friction is, $\mu =0.60$ .

The length of the muddy stretch is, $l=11\text{}\text{m}$ .

Formula Used:

The expression to calculate the acceleration of the cyclist to emerge from muddy stretch is,

  $a=-\mu g$

The expression to calculate the speed of the cyclist at the emerge from the muddy stretch is,

  $v=\sqrt{u^2+2al}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}a=-0.60\left(9.8\text{m}/{\text{s}}^2\right)\\ =-5.88\text{m}/{\text{s}}^2\end{array}$

Substitute all the values in the above expression.

  $\begin{array}{c}v=\sqrt{{\left(12\text{m}/\text{s}\right)}^2+2\left(-5.88\text{m}/{\text{s}}^2\right)\left(11\text{}\text{m}\right)}\\ =3.83\text{m}/\text{s}\end{array}$

Conclusion:

Thus, the cyclist will emerge from muddy stretch with acceleration $-5.88\text{m}/{\text{s}}^2$ and the speed of the cyclist at the emerge from the muddy stretch is $3.83\text{m}/\text{s}$ .