Kinematics with multiple objects

[Vontox7]

Homework Statement

Mike is standing below a tower. His friend on top of the tower which is 580 m drops a balloon at him. At the instant mike fires a potato from a cannon moving at an initial velocity of 95 m/s. How long does it take for the balloon and potato to collide?

Homework Equations

vf=vi+at
vf^2=vi^2+2ax
x=vi*t+0.5at^2
x=0.5(vi+vf)t

The Attempt at a Solution

What i did is split it into 2 parts one for the balloon and potato. The potato equation was
x=95t+0.5(-9.81)t^2
And the balloon equation as
x=0.5(9.81)t^2
and then i set them equal to each other and solved.
I got t=9.684 s

Homework Statement

Two cars initially 1 km apart are traveling towards each other. If Car A is traveling at 80 km/h east constantly and Car B accelerates at a rate of 10m/s^2 from rest. When will they pass each other and where?

Homework Equations

vf=vi+at
vf^2=vi^2+2ax
x=vi*t+0.5at^2
x=0.5(vi+vf)t

The Attempt at a Solution

I tried the same idea as i did before and got 22.2t=5t^2 and then t=4.44s and then i tried a different method by using systems of equations.
x=1000-10t
t=1000/22.2
subbed 1 into 2 and got 549.55m then subbed that into x=vi+0.5at^2 and got t=10.48s

 

[PhanthomJay]

For each problem. splitting into 2 parts is good, but you should note that the distances traveled in each part are not the same. For the potato problem, the balloon travels y meters and the potato travels (540-y) meters when they hit. Similarly, for the car problem, if car A travels x meters , car B travels (1000 - x) meters when they meet.