A projectile travels through the air with position $x = 15t$ and $y =-4.9t^2 + 46t + 11$ where $x$ and $y$ are measured in meters and $t$ is in seconds.

1. When does the projectile hit the ground?

   Hint (a):

   When does $y = 0$?

2. How far does the projectile travel during its trip through the air? That is, find the length of the path of the projectile.

3. What is the maximum height of the projectile?

   Hint (c):

   This is when $y^\prime = 0$.

4. Find the acceleration and velocity vectors of the projectile at time $t = 2$ seconds.