A projectile is launched from the ground at a $45°$ angle with altitude (in feet after $t$ seconds) given by $y(t) = 96t − 16t^2$ . Its horizontal displacement in feet is given by $x(t) =96t$.

1. Find an expression for the velocity vector as a function of $t$.

2. Calculate the magnitude of the velocity vector at $t = 0$ and at the moment when the projectile hits the ground. Make a conjecture about the speed with which projectiles return to earth.

   Hint (b):

   To determine when the projectile hits the ground, solve $0 = 96t – 16t^2$.
   The velocity vector when $t = 0$ is:
   Sketch this vector and use the Pythagorean Theorem to determine its magnitude.