What is the minimum speed required for Spiderman to catch a falling baby?

[Masrat_A]

Homework Statement

A baby falls from the top of a $45 m$ building. What is the minimum speed that Spiderman must push off from the same building one second later in order to catch the baby before she strikes the ground?

Homework Equations

Please see below.

The Attempt at a Solution

I tried my hand at solving to, unfortunately, no avail.

$v_{0y} - at = 0$
$10t = 45$
$t = 4.5$

$v_y = 45 - 10(4.5)$
$v_y = 0$

Here is the solution of a friend (which I feel is right), though he did not have enough time to explain his process.

$5t^2 +45 = 0$
$5t^2 = 45$
$t^2 = 9$
$t = 3 s$

$-5(2)^2 - v(2) +45 = 0$
$-20 - 2v + 45 = 0$
$25 - 2v = 0$
$2v = 25$
$v = 12.5$

Could anyone please explain to me what formulas had been used in the two parts to find time and velocity, and precisely how they were utilized?

 

[Orodruin]

$v_0y - at = 0$

I assume you meant to write $v_{0y}$. You should always provide your argumentation, otherwise it is not easy to decipher your thinking. Why do you think the appropriate expression should look like that?

Furthermore, what do you think is the reasoning behind the formulas your friend used? In order to learn it is also important to be able to look at a solution and decipher what it means. If you look at them, what are the formulas telling you?

(Your friend's result is correct - as long as you have the correct units - always quote the units!)

 

[Masrat_A]

I apologize; I've fixed it in my opening post.

I understand that time is needed for velocity, and once we're able to find the time of baby falling, we would have to subtract it by one for Spiderman. For the first part, could it be possible that he has used $h + 5t^2 = vt$? At $45 m$, our velocity would be $0$, so $vt$ equalling it does make sense.

For part two, after reviewing notes, it seems like the formula is $s = -5t^2 + vt + h$. I'm assuming $s$ is height of the ground, which is $0$.

What I'm now confused about, however, is why he had replaced the addition sign on the left of $vt$ in $s = -5t^2 + vt + h$ with subtraction.

 

[Orodruin]

The positive direction is the up direction, Spiderman clearly needs a speed in the down direction.

 

[Masrat_A]

That makes complete sense. Thank you very much!