Chapter 8.7, Problem 27PPS

a.

To determine

To calculation:

Resultant velocity of Camilla.

Answer to Problem 27PPS

Resultant velocity of Camilla is $7.76m/s$ .

Explanation of Solution

Given information:

Camilla is running at $100m$ dash at speed of $6.7m/s$ .

Speed of wind from behind $1.2m/s$

Calculation:

Initially find component form of wind vector.

  $\begin{array}{l}\cos 30°=\frac{y}{1.2}\\ y=1.2\cos °\\ y\approx 1.04\\ \sin 30°=\frac{x}{1.2}\\ x=\mathrm{1.2.}\sin 30\\ x=0.6\end{array}$

The wind vector is $\langle 6,1.04\rangle$

  

Since Camilla is running in a straight line her $x$ component is zero.

The Camilla’s vector is $\langle 0,6.7\rangle$

Add the winds vector with the Camilla’s vector.

  $\begin{array}{l}\langle .6+0,1.04+6.7\rangle \\ \langle .6,7.74\rangle \end{array}$

Now use Pythagoras theorem to find the resulting velocity.

  $\begin{array}{l}m=\sqrt{{.6}^2+{7.74}^2}\\ m=\sqrt{0.36+59.90}\\ m=\sqrt{60.29}\\ m=7.76m/s\end{array}$

Hence, Resultant velocity of Camilla is $7.76m/s$ .

b.

To determine

To calculation:

Time that Camilla will take to complete the dash.

Answer to Problem 27PPS

Time that Camilla will take to complete the dash is $12.89\sec onds$ .

Explanation of Solution

Given information:

Camilla is running at $100m$ dash at speed of $6.7m/s$ .

Speed of wind from behind $1.2m/s$

Calculation:

Initially find component form of wind vector.

  $\begin{array}{l}\cos 30°=\frac{y}{1.2}\\ y=1.2\cos °\\ y\approx 1.04\\ \sin 30°=\frac{x}{1.2}\\ x=\mathrm{1.2.}\sin 30\\ x=0.6\end{array}$

The wind vector is $\langle 6,1.04\rangle$

  

Since Camilla is running in a straight line her $x$ component is zero.

The Camilla’s vector is $\langle 0,6.7\rangle$

Add the winds vector with the Camilla’s vector.

  $\begin{array}{l}\langle .6+0,1.04+6.7\rangle \\ \langle .6,7.74\rangle \end{array}$

Now use Pythagoras theorem to find the resulting velocity.

  $\begin{array}{l}m=\sqrt{{.6}^2+{7.74}^2}\\ m=\sqrt{0.36+59.90}\\ m=\sqrt{60.29}\\ m=7.76m/s\end{array}$

Now, use dimensional analysis for finding out the time hat Camilla will take,

  $\frac{1s}{7.76m}.\frac{100m}{1}\approx 12.89\sec onds$

Hence, Time that Camilla will take to complete the dash is $12.89\sec onds$ .