Question

An 8-m-diameter hot air ballooon that has a total mass of 400 kg isstanding still in air on a windless day. The balloon suddenly is subjected to a 50 km/hrwind. Determine the initial acceleration of the balloon in the horizonal direction.

Answer 1

Answer:

The value of acceleration of the balloon a = 2.9 $\frac{m}{s^{2} }$

Explanation:

Diameter = 8 m

Mass = 400 kg

Speed V = 50$\frac{km}{hr}$ = 13.89 $\frac{m}{s}$

Coefficient of drag $C_D$ = 0.2 for air

Area = $\pi (4^{2} )$ = 50.24 $m^{2}$

We know that force on the balloon is given by

$F = \frac{1}{2} \rho A V^{2} C_D$

Put all the values in above equation we get

$F = \frac{1}{2} (1.2) (50.24) (13.89)^{2}$ × 0.2

F = 1163.15 N

Now acceleration of the balloon is given by

$a = \frac{F}{m}$

$a = \frac{1163.15}{400}$

a = 2.9 $\frac{m}{s^{2} }$

This is the value of acceleration of the balloon.