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A hot-air balloon with a mass of 400 kilograms moves across the sky with 3,200 joules of kinetic energy.

What's the velocity of the balloon? Use [tex]V=\sqrt{\frac{2KE}{m}}[/tex].

The velocity of the balloon is [tex]\boxed{\ \ \ }[/tex] meters/second.



Answer :

GinnyAnswer
To find the velocity of the hot-air balloon, we use the formula for velocity derived from kinetic energy:

[tex]\[ V = \sqrt{\frac{2KE}{m}} \][/tex]

Where:
- [tex]\( V \)[/tex] is the velocity of the balloon.
- [tex]\( KE \)[/tex] is the kinetic energy of the balloon.
- [tex]\( m \)[/tex] is the mass of the balloon.

Given data:
- The kinetic energy ([tex]\( KE \)[/tex]) is 3,200 joules.
- The mass ([tex]\( m \)[/tex]) is 400 kilograms.

Step-by-step, the calculation proceeds as follows:

1. Substitute the given values into the formula:
[tex]\[ V = \sqrt{\frac{2 \times 3200 \, \text{J}}{400 \, \text{kg}}} \][/tex]

2. Calculate the numerator of the fraction:
[tex]\[ 2 \times 3200 = 6400 \, \text{J} \][/tex]

3. Substitute this back into the formula:
[tex]\[ V = \sqrt{\frac{6400 \, \text{J}}{400 \, \text{kg}}} \][/tex]

4. Divide the numerator by the denominator:
[tex]\[ \frac{6400}{400} = 16 \, \text{m}^2/\text{s}^2 \][/tex]

5. Take the square root of the result:
[tex]\[ \sqrt{16 \, \text{m}^2/\text{s}^2} = 4.0 \, \text{m/s} \][/tex]

Therefore, the velocity of the balloon is [tex]\( 4.0 \)[/tex] meters per second.

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