Michael kicks a ball at an angle if 36* horizontal. its initial velocity is 46 m/s. find the maximum height it can reach, total time, and horizontal displacement for this motion

(a) At its maximum height, the ball's vertical velocity is 0. Recall that

Then at the maximum height , we have

(b) The time the ball spends in the air is twice the time it takes for the ball to reach its maximum height. The ball's vertical velocity is

and at its maximum height, so that

which would mean the ball spends a total of about 5.6 seconds in the air.

(c) The ball's horizontal position in the air is given by

so that after 5.6 seconds, it will have traversed a displacement of