The first antiparticle, the positron or antielectron, was discovered in 1932. It had been predicted by Paul Dirac in 1928, thoug
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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
1) The motion of the ball is an uniformly accelerated motion, with constant acceleration equal to 
(the negative sign means it is directed towards the ground).
For an uniformly accelerated motion, we can use the following relationship:
where h is the maximum height reached by the ball,
is its initial velocity and 
the velocity of the ball when it reaches the maximum height. But 
(when the ball reaches the maximum height, it stops before going down, so its velocity at that moment is zero), so we can use the relationship to calculate h, the maximum height:
2) We can find the time the ball takes to return to the ground by requiring that the space covered by the ball returns to zero:
where for an uniformly accelerated motion,
By solving this, we have two solutions: one is t=0, which corresponds to the moment the player hits the ball, the second one is
so, the ball returns to the ground after 4 s.
3) The velocity of the ball when it returns to the ground is given by:
where the negative sign means the ball is going downwards.
For an uniformly accelerated motion, we can use the following relationship:
where h is the maximum height reached by the ball,
2) We can find the time the ball takes to return to the ground by requiring that the space covered by the ball returns to zero:
where for an uniformly accelerated motion,
By solving this, we have two solutions: one is t=0, which corresponds to the moment the player hits the ball, the second one is
so, the ball returns to the ground after 4 s.
3) The velocity of the ball when it returns to the ground is given by:
where the negative sign means the ball is going downwards.