Object A (in free fall) hits object B (ascending with constant velocity)

[bob012345]

Ok, let me try this...
$h - vt - \frac 1 2 g t^2 = 0$
$$ ax^2 + bx + c = 0 $$

What's your final answer for t?

 

[PeroK]

???
Please try it on your own:
H = 2m
v = 5.833 m/s
g = 9.8 m/s²

Solve the equation for t...

You could always have checked this on a spreadsheet. You want to find $t$ such that:
$$5.833t + \frac 1 2 9.8 t^2 = 2$$You could start at $t = 0.01$ and go up in increments of $0.01$ until you get to $2$:

u	g
5.833​	9.8​
t	ut	1/2 gt^2	d
0.01​	0.05833​	0.00049​	0.05882​
0.02​	0.11666​	0.00196​	0.11862​
0.03​	0.17499​	0.00441​	0.1794​
0.04​	0.23332​	0.00784​	0.24116​
0.05​	0.29165​	0.01225​	0.3039​

 

[Lnewqban]

@groetschel
For a different approach to the same problem, please see:
https://www.physicsclassroom.com/class/1DKin/Lesson-5/Representing-Free-Fall-by-Graphs#:~:text=Representing Free Fall by Velocity-Time Graphs&text=As learned earlier, a diagonal,time graph would be diagonal.

 

[bob012345]

Ok, let me try this...
$h - vt - \frac 1 2 g t^2 = 0$
$$ ax^2 + bx + c = 0 $$

Put the first into the form of the second and identify what is a,b and c. Then use the formula given earlier for the quadratic in terms of a,b,c to solve for t (or x if that's easier).