Kinematics- Vertical Motion

Need some help with a physics problem. Thanks!

Mitch is skydiving, he jumps out of the plane and reaches a terminal velocity of 20 m/s. When he is 1000 m above the ground, Skid, standing directly below Mitch fires a rocket at Mitch. The rocket has an initial velocity of 125 m/s.

a) How much time does Mitch have to figure out how to survive this predicament?

b) Assuming Mitch does not have his wits about him, at what location above the ground will the rocket intersect with him?

Y= Yo + Vot + 1/2at^2

V= Vo + at

V^2= Vo^2 + 2a△Y

I know that two separate equations are necessary and that setting them equal to each other will give me the answer, however I still need a bit of guidance. Thanks again!

and here are the variables that are given and assumed (i think)

Mitch: Yo= 1000m V= 20m/s a= 0m/s^2

Rocket: Yo= 0m Vo= 125 m/s a=-9.8m/s^2

Re: Kinematics- Vertical Motion

I repeatedly see problems like this and **dislike** them for one simple reason- they **don't** mean "rocket"! The whole point of a rocket is that they have an engine on board and can continue to accelerate, or at least not decelerate just with the acceleration due to gravity. But here, you are only given that the initial velocity so they must be talking about something **thrown** or **fired** upward.

Yes, Mitch is falling downward with, as you say, "Yo= 1000m V= 20m/s a= 0m/s^2" so that the formula Y= Yo + Vot + 1/2at^2 becomes Y= 1000- 20t. The "rocket" ("rock" might be better!) has Yo= 0m Vo= 125 m/s a=-9.8m/s^2 so Y= 125t- (9.8/2)t^2= 125t- 4.9t^2.

The rock will hit Mitch when he and the rock have the same height: 1000- 2t= 125t-4.9t^2. Solve that for t.