# Question 15.11: A man descends to the ground from an aircraft with the help ......

A man descends to the ground from an aircraft with the help of a hemispherical parachute of 3 m diameter against the resistance of air. If the weight of the man is 690 N, find the velocity of parachute with which it comes down. The density of air is $1.2 \mathrm{~kg} / \mathrm{m}^3 \text { and. } C_D=0.4$ for the hemisphere.

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Given data:

Diameter of parachute                          D = 3 m

Weight of man                                        W = 690 N
Coefficient of drag                                  $C_D=0.4$

Density of air 1.2 kg/m³

Projected area is                                    $A=\frac{\pi}{4} D^2=\frac{\pi}{4}(3)^2=7.068 \mathrm{~m}^2$

The total weight of the man is balanced by the drag force. Thus, the drag force is

$F_D=W=690 \mathrm{~N}$

Let the velocity of parachute be U.

From Eq. (15.14), we have

$F_{D}=C_{D}A\frac{1}{2}\rho U_{∞}^{2}$  (15.14)

$F_D=C_D A \frac{1}{2} \rho U^2$

or                                  $U=\sqrt{\frac{F_D \times 2}{C_D A \rho}}=\sqrt{\frac{690 \times 2}{0.4 \times 7.068 \times 1.2}}=20.168 \mathrm{~m} / \mathrm{s}$

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