CPM Homework Help : CALC Problem 11-67

Pete Moss is reviewing his notes again, 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 $\it{t = 3}$ seconds. The ball's horizontal position $\it{x(t)}$ and the height $\it{y(t)}$ (measured in feet) is shown below. The ball will be caught $6$ feet above the ground by Pete Moss.

$x(t) = 40t − 120$
$y(t) = −16t^2 + 144t − 282$

Find the velocity and speed of the football when Pete catches it.
Hint (a):
See the homework help for 11-57 (a).
speed = |velocity|, or the length of the velocity vector (when $t = 6$ )
Specify the direction the football was traveling in when Pete catches it.
Hint (b):
Sketch the velocity vector from part (a).
Use inverse tangent to determine the direction of the vector.