Can anyone solve these for my by using unit vectors? can you also show your work

4. The Coyote has an initial position vector of .

4a. The Coyote has an initial velocity vector of . His position at time is given by the vector

where is the Coyote's acceleration vector at time . He experiences acceleration only in the downward direction because of gravity, and in particular where . Splitting up the position vector into components, we have with

The Coyote hits the ground when :

4b. Here we evaluate at the time found in (4a).

5. The shell has initial position vector , and we're told that after some time the bullet (now separated from the shell) has a position of .

5a. The vertical component of the shell's position vector is

We find the shell hits the ground at

5b. The horizontal component of the bullet's position vector is

where is the muzzle velocity of the bullet. It traveled 3500 m in the time it took the shell to fall to the ground, so we can solve for :