26. a ball is kicked with an initial velocity of 16 m/s in the horizontal direction and 12 m/s in the vertical direction. (a) at what speed does the ball hit the ground? (b) for how long does the ball remain in the air? (c)what maximum height is attained by the ball?

The given problem models a parabolic motion, where the intial speed is the same as the final speed when the ball hits the ground, assuming that there's no wind.

So, by given we already know the horizontal and vertical initial velocities, which are

Now, to find the initial velocity (which is equal to the velocity when hits the ground), we need to sum both vector magnitues with the following formula

To find the time thorugh which the ball remains in the air, we need to find the times that took to reach the highest point, and then we duplicate it, because the movement is vertically symmetrical. So, the tima to the highest point is defined as

Where, and .

(Remember that we need to use the vertical initial velocity, beacuse the times to get to the highest points depends on vertical magnitudes).

Replacing all values, we have

So, the time while the ball was in the air is

The last question is about the highest point the ball reached, that can be found with

Replacing all values, we have

Therefore,