CPM Homework Help : APCALC Problem 11-56

Pete Moss is reviewing his notes from his football coach, shown below. He knows he needs to catch the ball when $t = 6$ , three seconds after the quarterback throws the pass.

Coach’s Notes:

Artfish L. Turf will throw the football at $t = 3$ seconds. The ball’s horizontal position $x(t)$ and the height $y(t)$ (measured in feet) are shown at right. The ball will be caught $6$ feet above the ground by Pete Moss.

$x\left(t\right) = 40t − 120$

$y\left(t\right) = −16t^{2} + 144t − 282$

Write the general velocity and acceleration vectors for the ball’s flight.
Hint (a):
$\vec{v(t)}=\langle x^\prime(t),y^\prime(t)\rangle$
$\vec{a(t)}=\langle x^{\prime\prime}(t),y^{\prime\prime}(t)\rangle$
Calculate the velocity and acceleration of the ball when the catch is made.
Hint (b):
Evaluate each of the vectors from part (a) for $t = 6$ .