Answer:
The value of acceleration of the balloon a = 2.9 [tex]\frac{m}{s^{2} }[/tex]
Explanation:
Diameter = 8 m
Mass = 400 kg
Speed V = 50[tex]\frac{km}{hr}[/tex] = 13.89 [tex]\frac{m}{s}[/tex]
Coefficient of drag [tex]C_D[/tex] = 0.2 for air
Area = [tex]\pi (4^{2} )[/tex] = 50.24 [tex]m^{2}[/tex]
We know that force on the balloon is given by
[tex]F = \frac{1}{2} \rho A V^{2} C_D[/tex]
Put all the values in above equation we get
[tex]F = \frac{1}{2} (1.2) (50.24) (13.89)^{2}[/tex] × 0.2
F = 1163.15 N
Now acceleration of the balloon is given by
[tex]a = \frac{F}{m}[/tex]
[tex]a = \frac{1163.15}{400}[/tex]
a = 2.9 [tex]\frac{m}{s^{2} }[/tex]
This is the value of acceleration of the balloon.
