Question

A baseball is hit almost straight up into the air with a speed of 22m/s. Estimate how high it goes and how ling it is in the air

Answer 1

looks like "almost straight up" should be considered as 90º angle for the initial velocity, i.e. only y-component, in such case the velocity for the ball at any time is:
\[v(t)=v_0-gt\]
in this case \(v_0=22m/s\)
the height of the ball at anytime is given by:
\[y(t)=y_0+v_0t-\frac{1}{2}gt^2\]
to determine the time it takes to get to the highest point \(H\) we can set the speed to 0, since at that point the ball stops for an instant:
\[v_0-gt=0\]
with the time we get from that eq. we can calculate \(H\) using the equation for \(y(t)\)
give it a try!