Solve 1D Relative Motion Homework: Ball Thrown, Elevator, Tennis & Baseballs

[shizaep]

Homework Statement

1)A ball is dropped from the top of a 56.0 m-tall building. After 2.00 s, another ball is thrown upward from the ground. When the two balls pass the same point, they have the same speed. How fast was the upward-bound ball thrown?

2)You are riding an elevator with an open roof. You are moving down at a speed of 4.00 m/s when you throw an apple up into the air at a speed of 6.00 m/s relative to the elevator.
a) How long does it take you to catch the apple?

3)A child has a tennis ball and a baseball. He let's go of the tennis ball from the top of a high building, waits , and then throws the baseball straight down with a speed such that the two balls have a relative speed of 10 m/s when they meet 40 m below. How long did the child wait before throwing the baseball?

4) You throw a ball up in the air with a speed such that it reaches your friend on a balcony 30.0 m above. At the same time, your friend throws another ball down to you such that it reaches you with twice the speed with which you threw your ball. What is the relative velocity of the two balls when they pass each other?

Answers:
1)33.1 m/s
2)a)1.77s
3)??
4)37 m/s

Homework Equations

v_f²-v₀²=2a*Δx

x₁₂=1/2*a₁₂t^2 + v_0,12t + x_{0, 12}

v_f = v₀ + at

The Attempt at a Solution

I spent a lot of time trying all of these, my attempts are in a notebook

Basically, I just have trouble modelling the relationship, if you set up the equation with like 1 line of explanation I will likely be able to follow it

Thanks to anyone who helps me with 1/more problems

 

[voko]

Let's take problem #1.

The balls meet at some time t. They meet at displacement x (let's place the origin at the ground). The ball going down has velocity -v, the ball going up has velocity v.

Write the equations relating t, v and x for both balls.

 

[shizaep]

ok, so what i did first is write the velocity and position for the dropped ball 2.00 seconds into its' "flight":

v_f = -19.62 m/s (i choose up to be positive here)
x_f = 36.4 m (above origin)

so now i guess they're in the"state" where they can be related using a relative equation

x₁₂ = 0 + 0 + x

??
this is where i am confused. relative acceleration is zero so therefore the relative speed should always be constant?

 

[voko]

Why do you care where the dropped ball is in 2 seconds and what its velocity is? You are given the condition for its location and displacement at some later time t. It is unknown, so you end up having two equations for the dropped ball. Likewise, you will have equations for the other ball. Write them down.

 

[Gank]

What would the distance they meet be?