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

A hot-air balloon with a mass of 400 kilograms moves across the sky with 3,200 joules of kinetic energy. The velocity of the balloon is ____ meters/second.

Sagot :

GinnyAnsweridn
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.
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