Finding the time of arrival between two balls in air using kinematics

[garcia1]

Homework Statement

A ball is thrown upward from the ground with
an initial speed of 51 m/s; at the same instant,
a ball is dropped from a building 38 m high.
After how long will the balls be at the
same height? The acceleration of gravity is
9.8 m/s2 .
Answer in units of s.

Homework Equations

Equations of Kinematics

The Attempt at a Solution

I thought that by finding the time difference between the two that it would give me the answer.

Setting up the equation as DeltaT = T1 - T2, I found the times for each object using equation Vf = Vi + at for the object with a velocity of 51m/s, and the equation x = Vo*t + 1/2at^2 for the object 38 meters above the ground. Finding the time for these two, I plugged them into my DeltaT equation, with the biggest value as T1.

I got the answer 2.42s, but this was wrong.

 

[tiny-tim]

hi garcia1!

Setting up the equation as DeltaT = T1 - T2, I found the times for each object using equation Vf = Vi + at for the object with a velocity of 51m/s …

i don't understand … how do you know V_f ?

why not use the same equation for both balls (with different x₀ and v₀ of course)?

 

[garcia1]

What I thought you meant by this was that I should set both equations equal to a common variable, and then solve for T accordingly. I tried this with the variable Vf, solving for both in this way:

Eq 1: Vf = Vo +at
Eq 2: Vf^2 = Vo^2 + 2ax -> Vf = rad(Vo^2 + 2ax)

Then setting them equal to each other: Vo + at = rad(Vo^2 + 2ax) - Vo
a

I solved for t, and got the answer T = 2.42s, but this was wrong. Any thoughts on where I messed up?

 

[garcia1]

The second equation is over a. Sorry, computing error.

 

[gneill]

You're trying to find when both balls will be at the same height. So wouldn't it be a good idea to write an equation for each ball which gives the height at a given time and then equate them?

 

[tiny-tim]

hi garcia1!

(just got up :zzz: …)

What I thought you meant by this was that I should set both equations equal to a common variable, and then solve for T accordingly. I tried this with the variable Vf …

but that will only give you the time T at which they both have the same velocity, won't it?