### Home > APCALC > Chapter 11 > Lesson 11.2.3 > Problem11-67

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 $t = 3$ seconds. The ball’s horizontal position $x(t)$ and the height $y(t)$ (measured in feet) is shown at right. The ball will be caught $6$ feet above the ground by Pete Moss.$x(t) = 40t − 120$$y(t) = -16t2 + 144t - 282$
1. What are the velocity vector and speed of the football when Pete catches it?

See the homework help for 11-57 (a).
$\text{speed} = \left|\text{velocity}\right|$, or the length of the velocity vector (when $t = 6$)

2. Specify the direction the football is traveling in when Pete catches it.

Sketch the velocity vector from part (a).
Use inverse tangent to determine the direction of the vector.

$\tan^{-1}\Big(\frac{y^\prime(6)}{x^\prime(6)}\Big)$