Certainly! To find the velocity of the hot-air balloon, we will use the formula for kinetic energy that relates mass, kinetic energy, and velocity. The formula is:
[tex]\[ V = \sqrt{\frac{2KE}{m}} \][/tex]
Where:
- [tex]\( V \)[/tex] is the velocity,
- [tex]\( KE \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass.
Given:
- Mass ([tex]\( m \)[/tex]) = 400 kilograms,
- Kinetic energy ([tex]\( KE \)[/tex]) = 3200 joules.
Let's substitute the given values into the formula:
[tex]\[ V = \sqrt{\frac{2 \times 3200}{400}} \][/tex]
First, calculate the numerator:
[tex]\[ 2 \times 3200 = 6400 \][/tex]
Next, divide by the mass:
[tex]\[ \frac{6400}{400} = 16 \][/tex]
Finally, take the square root:
[tex]\[ V = \sqrt{16} = 4 \][/tex]
Thus, the velocity of the balloon is [tex]\( 4 \)[/tex] meters per second.
