### Home > APCALC > Chapter 11 > Lesson 11.2.2 > Problem11-56

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$
1. Write the general velocity and acceleration vectors for the ball’s flight.

$\vec{v(t)}=\langle x^\prime(t),y^\prime(t)\rangle$

$\vec{a(t)}=\langle x^{\prime\prime}(t),y^{\prime\prime}(t)\rangle$

2. Calculate the velocity and acceleration of the ball when the catch is made.

Evaluate each of the vectors from part (a) for $t = 6$.