## Minimum Speed

**With what minimum speed must you toss a 100 ball straight up to hit the 14 -high roof of the gymnasium if you release the ball 1.4 above the ground?
Solve this problem using energy.**

Work is the same as change in energy

You can figure out how much gravitational potential energy the ball has when it is 15.0 m above the ground by using

W = KE = mgh

Difference of the heights;

14-1.4=12.6

**W = KE =** (.100 kg) * (9.81 m/s^{2}) * (12.60 m) = 12.3606 J

That’s how much kinetic energy the ball will need to reach a height of 14.0 meters

There’s another equation for kinetic energy which is KE = 1/2 m v^{2}

Use that to solve for velocity

v^{2} = KE / (1/2 * m)

v = √ (KE / (1/2 * m) )

= √ (12.606 J / (1/2 * .100kg) )

= 15.87m/s

The speed that it is shot up will also be the speed that it hits the ground, since energy is conserved

**2) With what speed does the ball hit the ground?**

**Vf**

^{2}= Vi + 2ax**Vf**

^{2}= 0 + 2 (9.8) (14m)**Vf ^{2} **= 274

**Vf**= √274

**Vf**= 17 m/s

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