Question 12.45: During a high-speed chase, a 2400-lb sports car traveling at...

(a) Note: \quad 100 \mathrm{\ mi} / \mathrm{h}=146.667 \mathrm{\ ft} / \mathrm{s}

+\downarrow \Sigma F_{n}=m a_{n}: \quad W_{\text {car }}  =\frac{W_{\text {car }}}{g} \frac{\nu_{A}^{2}}{\rho}

or 

\begin{aligned}\rho & =\frac{(146.667 \mathrm{~ft} / \mathrm{s})^{2}}{32.2 \mathrm{\ ft} / \mathrm{s}^{2}} \\& =668.05 \mathrm{\ ft}\end{aligned}

or \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\rho=668 \mathrm{\ ft}\blacktriangleleft

(b) Note: \nu is constant \Rightarrow a_{t}=0 ; 50 \mathrm{\ mi} / \mathrm{h}=73.333 \mathrm{\ ft} / \mathrm{s}

+\downarrow \Sigma F_{n}=m a_{n}: \quad W-N =\frac{W}{g} \frac{\nu_{A}^{2}}{\rho}

or \quad N =(160 \mathrm{\ lb})\left[1-\frac{(73.333 \mathrm{\ ft} / \mathrm{s})^{2}}{\left(32.2 \mathrm{\ ft} / \mathrm{s}^{2}\right)(668.05 \mathrm{\ ft})}\right]

or \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\mathbf{N}=120.0 \mathrm{\ lb}\uparrow\blacktriangleleft