find function and solve max problem
Suppose this fox wants to try and kill a rabbit. He has a catapult which is capable of launching a rock at 70 m/s. The fox found a completely flat spot on cartoon land (which he labelled as X). He wants to place the catapult so that it is due west of X. Further, he wants to try get as far away from X as he can to be safe. The only force acting on the rock is gravity; on cartoon land, it has a constant downward component of 8.75 m/s^2, and a constant westerly component of 3.5 m/s^2. There is no southerly component to take into account.
1.) What's the angle from the horizontal that the fox should aim the catapult in order to maximize the distance that the rock will travel. Give the max. distance. What is the plot of the path that the rock will go on?
2.) What's the angle the fox should avoid to prevent getting hit by the rock. Give the plot of this path that the fox does NOT want the rabbit to take.