Asoccer ball is kicked with an initial speed of 8.8 m/s. after 0.179 s it is at its highest point. what was its initial direction of motion? ,

To solve the problem we can consider only the motion on the vertical direction (y-axis). Let's the take upward as positive direction, such that the acceleration of the motion (the gravitational acceleration) is negative: , because it is against the direction of the motion.
The initial speed of the ball on the y-axis is , where and where is the angle of the initial velocity v0 with respect to the horizontal, so it's the direction that we want to find.

The law of the velocity on the y-axis is:

Where t is the time. At its highest point, the vertical velocity of the ball is zero, and this occurs when t=0.179 s: . So we can write:

And substituting the numbers we can find the value of the angle:

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