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

The value of acceleration of the balloon a = 2.9
`(m)/(s^(2) )`

Step-by-step explanation:

Diameter = 8 m

Mass = 400 kg

Speed V = 50
`(km)/(hr)` = 13.89
`(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 = (1)/(2) \rho A V^(2) C_D`

Put all the values in above equation we get

`F = (1)/(2) (1.2) (50.24) (13.89)^(2)` × 0.2

F = 1163.15 N

Now acceleration of the balloon is given by

`a = (F)/(m)`

`a = (1163.15)/(400)`

a = 2.9
`(m)/(s^(2) )`

This is the value of acceleration of the balloon.