A ball is thrown off of a roof with a velocity of $75$ ft/s at an angle of $50^\circ$ with the horizontal. It is released from a height of $35$ ft above the ground.

1. Write a set of parametric equations to model the position of the ball in relationship to its starting position at any time $t$ seconds after it was thrown.

   Hint (a):

   An object that is launched with an initial position of $\left(x_0,y_0\right)$ and an initial velocity of $v_0$ and an angle of $\theta$ will travel along a path defined by the parametric function: 

   $x\left(t\right)=\left(v_0\cos\left(\theta\right)\right)t + x_0$
   $y\left(t\right)=-16t^2 + \left(v_0\sin\left(\theta\right)\right)t + y_0$

   where $x$ and $y$ are measured in feet and $t$ is measured in seconds.

2. How far does the ball travel horizontally before it hits the ground?

   Hint (b):

   The ball hits the ground when $y\left(t\right) = 0$. Solve that equation first.
   Then compute $x\left(t\right)$ using the time at which the ball hit the ground.