A strange kind of straight line kinematics with uniform acceleration.

[ZamielTheGrey]

Homework Statement

A ball is thrown upward from a building 30 meters tall and misses the edge on its way down, hitting the ground 6 seconds after it was thrown.

A) With what speed was it thrown?
B) What is its highest height?

Homework Equations

Vf = Vi + at
x = 1/2(Vi + Vf)
x = Vi t + 1/2(at^2)
Vf^2 = Vi^2 + 2ax

Vf = final velocity
Vi = initial velocity
a = acceleration
x = distance
t = time

The Attempt at a Solution

So, it is a two part problem, the upward motion, and then the downward.
I will label the distance from being thrown to the highest point of the arc as x₁, which is also the same distance down to being level with where it was thrown from, and then x₂ is 30 meters.

Thus goes that to find time, I need to use x = Vi t + 1/2(at^2).
x_total = x₁+30
Vi = 0
t₂ = 6 - t₁
a = 10 (lets make positive downward)

So here I am stumped by the fact that I do not have three known variable to make use of the equation. How am I supposed to proceed?

 

[lewando]

Make use of this form of the equation.

x = x₀ + v₀t + 0.5at²

[edit- you are trying to find v₀]

 

[ZamielTheGrey]

Yeah... so we have two missing variable then. An X and Vo :O

 

[lewando]

If the x-axis represents height, you know x₀ and you know the final x. v₀ is the only unknown. Totally solvable.

 

[ZamielTheGrey]

If I take the base of the skyscraper as the start of the x axis, the ball is thrown up from 30m.

x₀ = 30m
x_final= 0

That completely ignores the up and then down arc of the ball, what am I not understanding?

 

[lewando]

The up and down arc is not relevant. Let the equation do the work.

[edit-- "a = 10 (lets make positive downward)". If +x is pointing up, then a should be negative.]

 

[ZamielTheGrey]

So...

x = x0 + v0t + 0.5at2
-30 = V₀ + 0.5*(-10*6²)
-30 = V₀ - 180
150 = V₀

Is this it?

 

[lewando]

Close! You dropped the "t" from v₀.

 

[ZamielTheGrey]

Oh, oops.

x = x0 + v0t + 0.5at2
-30 = V0*6 + 0.5*(-10*62)
-30 = V0*6 - 180
150 = V0*6
V0 = 25

Alright, great, thanks. The second part I can easily do on my own. :)

 

[lewando]

Good!