Can a Stuntman Jump Safely into a Pool from a 50-Meter Building?

[Alimarin]

Homework Statement

A stuntman must jump in a pool from a 50.0 meter tall building. The pool is a horizontal distance of 21.0 meters from the base of the building.

a) What is the initial velocity of the stuntman to be able to land in the pool?
b) Do you think this velocity is reasonable for a human?
c) Realistically, how tall must this building be for the stuntman to be able to make the landing safely?

Homework Equations

Vf^2 = Vi^2 + 2aΔx
Vf = Vi + aΔt
Xf-Xi = Δx
Given:
Xix = 0m
Xfx = 21m
Xiy = 50m
Xfy = 0m
Δx = 21m
Δy = -50m
a= -9.81m/s^2
Viγ = 0m/s

Relevant Unknowns:
Δt = ?
Vfγ = ?

The Attempt at a Solution

Vf^2 = Vi^2 + 2aΔx
Vf^2 = 0^2 + 2(-9.81m/s^2)(-50m)
Vf^2 = 2(9.81m/s^2)(50m)
Vf^2 = 981
Vf = 31.3 m/s

Vf = Vi + aΔt
31.3 = 0 + (-9.81m/s^2) Δt
31.3 = -9.81m/s^2 (Δt)
31.3 = Δt
-9.81m/s^2

Yeah, you see the issue, I made a stupid mistake and my brain is on 0 hours of sleep. and I have school in 1 hour.

 

[BruceW]

You were close, Vf^2 = 981 is right. But then you chose the positive root. The actual answer is the negative root Vf = -31.3 because the stuntman is falling downwards. So the change in time is the positive value of the answer you got.

 

[Alimarin]

You were close, Vf^2 = 981 is right. But then you chose the positive root. The actual answer is the negative root Vf = -31.3 because the stuntman is falling downwards.

But mathematically that would take me into irrational numbers, E.g. 31.3i

Which would mean I would have to do some algebraic things I don't even remember how to do anymore.

I just realized that square roots have a + or -, never mind.

See? My brain doesn't have it's sensitivity to serotonin at the moment.

 

[BruceW]

No worries, good luck finishing the question.

 

[Alimarin]

Alright, this time I did it right.

Garcias