Chapter 6.2, Problem 43PPE

(a)

To determine

Time taken by Pam to catch up to Michelle.

Answer to Problem 43PPE

0.51sec were taken by Pam to catch up to Michelle.

Explanation of Solution

Given data:

Total path distance =200m

Speed of Pam $7.5m/s$

Speed of Michelle $7.8m/s$

Formula used:

  $speed=\frac{dis\tan ce}{time}$

Calculation:

Let the distance covered at time t be d

For Pam

  $\begin{array}{l}7.5=\frac{d}{t}\\ 7.5t_{pam}=d_{pam}\end{array}$

For Michelle:

  $\begin{array}{l}7.8=\frac{d}{t}\\ 7.8t_{michelle}=d_{michelle}\end{array}$

  $t_{pam}=1+t_{michelle}$

For catching the Michelle

  $\begin{array}{l}{d}_{pam}=d_{michelle}\\ 7.5t_{pam}=7.8t_{michelle}\\ 7.5t_{pam}=7.8(1-t_{pam})\\ 7.5t_{pam}=7.8-7.8t_{pam}\\ 7.5t_{pam}+7.8t_{pam}=7.8\\ 15.3t_{pam}=7.8\\ t_{pam}=0.51\sec \end{array}$

Conclusion:

0.51sec were taken by Pam to catch up to Michelle.

(b)

To determine

Will Pam overtake Michelle before finish line.

Answer to Problem 43PPE

Pam can`t overtake Michelle.

Explanation of Solution

Given data:

Total path distance =200m

Speed of Pam $7.5m/s$

Speed of Michelle $7.8m/s$

Calculation:

Time taken by Pam:

  $\begin{array}{l}7.5=\frac{200}{t}\\ t=\frac{200}{7.5}\\ t=26.6\sec \end{array}$

Time taken by Michelle:

  $\begin{array}{l}7.8=\frac{200}{t}\\ t=\frac{200}{7.8}\\ t=25.5\sec \end{array}$

Conclusion:

As the Pam takes more time than Michelle so Pam can`t overtake Michelle.