Question

The drag force Fd, imposed by the surrounding air on a vehicle moving with velocity V is given by:

Answer 1

Answer:

Explanation:

a)

Given that:

V = 25 mi/hr

To ft/sec, we have:

$V = 25 \times \dfrac{5280}{3600} ft/s$

$V = \dfrac{110}{3} ft/s$

$\rho = 0.075 \ lb/ft^3$

$\rho = 0.075 \times \dfrac{1 \ lbf s^2/ft}{32.174 \ lbm}$

$\rho = \dfrac{0.075}{32.174 } lbf.s^2/ft^4$

$C_d = 0.28$

A = 25ft²

Recall that:

The drag force $F_d =\dfrac{C_dA \rho V^2}{2}$

$F_d =\dfrac{1}{2}\times 0.28 \times 25\times \dfrac{0.075}{32.174}\times (\dfrac{110}{3})^2$

$F_d =10.967 \ lbf$

$P = F_dV \\ \\ P = 10.97 \times (\dfrac{110}{3}} \\ \\ P = 402.3 \ hp$

For 70 miles per hour, we have:

$V = 70 \times \dfrac{5280}{3600} ft/s$

$V = \dfrac{308}{3} ft/s$

The drag force $F_d =\dfrac{C_dA \rho V^2}{2}$

$F_d =\dfrac{1}{2}\times 0.28 \times 25\times \dfrac{0.075}{32.174}\times (\dfrac{308}{3})^2$

$F_d =85.99 \ lbf$

$P = F_dV \\ \\ P = 85.99 \times (\dfrac{308}{3}}) \\ \\ P = 8828.2 \ hp$