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