With what minimum speed must you toss a 200 g ball straight up to just touch the 14-m-high roof of the gymnasium if you release the ball 1.3 m above the ground? solve this problem using energy.

When they say use energy, you want to use

Total energy = potential energy + kinetic energy = mgh + 1/2mv²

I assume you mean 200 g ball,

so, we know the total distance traveled is going to be 13 - 1.3 = 11.7 m

If the ball just makes it to the top ( 13 m ) , then the ball will stop moving and the kinetic energy will be 0,

therefore, the potential energy at the top will be the total energy of the system = mgh

from this, we say that mgh = 1/2mv² solve for v

v = sqrt (2gh) = 15.2 m/s