Given that a boy throws a ball horizontally from the top of a building with an initial speed of $31 \, \text{m/s}$, we are asked to find the horizontal and vertical velocity of the ball after 22 seconds. We will assume the motion takes place in the absence of air resistance.

Horizontal Velocity:

The horizontal velocity remains constant in the absence of air resistance since there are no forces acting horizontally (assuming ideal conditions). Therefore, the horizontal velocity remains the same as the initial velocity: $v_x = 31 \, \text{m/s}$

Vertical Velocity:

The vertical velocity is affected by gravity. The initial vertical velocity $v_{y0}$ is zero since the ball is thrown horizontally. The vertical velocity after time $t$ is given by: [ v_y = v_{y0} + g \cd