Xavier is roller skating at 14 km/h and tosses a set of keys forward on the ground at 8 km/h. The speed of the keys relative to
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(a) The ball has a final velocity vector
with horizontal and vertical components, respectively,
The horizontal component of the ball's velocity is constant throughout its trajectory, so , and the horizontal distance <em>x</em> that it covers after time <em>t</em> is
It lands 103 m away from where it's hit, so we can determine the time it it spends in the air:
The vertical component of the ball's velocity at time <em>t</em> is
where <em>g</em> = 9.80 m/s² is the magnitude of the acceleration due to gravity. Solve for the vertical component of the initial velocity:
So, the initial velocity vector is
which carries an initial speed of
and direction <em>θ</em> such that
(b) I assume you're supposed to find the height of the ball when it lands in the seats. The ball's height <em>y</em> at time <em>t</em> is
so that when it lands in the seats at <em>t</em> ≈ 6.38 s, it has a height of