You are rolling on a skateboard with a constant velocity of 12 m/s. as you are moving you toss a baseball straight up into the air with a vertical speed of 25 m/s.

how long will it take the ball to land back in your hand?

how high will the ball go before it falls back what is its peak height?

Your horizontal motion has no effect on the answers.
Your sister is standing on the sidewalk as you skate by.
At the same exact instant that you toss yours, she tosses
another baseball straight up at 25 m/s, and she gets exactly
the same answers as you get.

The acceleration of gravity is 9.8 m/s² down, so each baseball
loses 9.8 m/s of upward speed each second after you toss them.
They can only continue going up for  (25/9.8) = 2.55 seconds.
At that point, each ball has run out of upward gas, stops, turns
around, and starts falling.  It takes the same 2.55 seconds to
return to the same height from which it was tossed.  So each
ball takes (2 x 2.55) = 5.1 seconds to land back in your hands.

The average speed of each ball on the way up is

                (1/2) (speed at the bottom + speed at the top)

             = (1/2) (25 + 0)  =  12.5 m/s ,

and it spends 2.55 seconds rising.

The distance it covers upward is 

                           (average speed) x (time)

                        =      (12.5 m/s)  x  (2.55 sec)

                        =           31.875 meters .

There it is.  The physics and math are bullet-proof, but
the numbers are whacko.

From a skateboard, you tossed a baseball straight up
at  56 miles per hour ... fast enough for it to reach 105 feet,
possibly the height of a 7-story building, before it falls back !

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