Comparing Vertical Velocities of Identical Balls Thrown from Different Heights

[student 1]

Homework Statement

A person standing on top of a building of height H throws a ball vertically upward with initial velocity Vj. He then throws an identical ball vertically downward with initial velocity -Vj. Compare the velocities of the two balls just before they strike the ground. Write equations to explain your reasoning.

Homework Equations

Vf=Vi+At
Yf=Yi+Vit-At^2
Acceleration=-9.8 m/s^2
Velocity at time T=4.9t^2

The Attempt at a Solution

I know that at the point when the first ball gets back to y=0 the velocities are the same. I do not know how to keep comparing them to show the balls are the same just before they hit the ground. Any help is appreciated!

 

[Kurdt]

You'll be bettor off using other constant acceleration equations involving initial and final velocities and the acceleration and distance since you don't have the time in this question. It should then become obvious.

 

[student 1]

I don't know what equations to use if I don't use these. The teacher said this is all you would need but if there is a more simple way I'm willing to use it!

 

[alphysicist]

Hi student 1,

I think there are some inaccuracies with your relevant equations. You have:

Homework Equations

Vf=Vi+At
Yf=Yi+Vit-At^2
Acceleration=-9.8 m/s^2
Velocity at time T=4.9t^2

The first and third are okay. You're missing a factor in the second equation, and the fourth equation is wrong. These should be:

$$\begin{align} v_f &= v_i + a t \nonumber\\ y_f &= y_i + v_i t + \frac{1}{2} a t^2\nonumber\\ a &= - 9.8 \mbox{ m/s^2 for free fall near Earth's surface}\nonumber \end{align}$$

The other equation that Kurdt mentioned that is very useful for these problems is

$$v_f^2 = v_i^2 + 2 a (\Delta y)$$

There are 2 more constant-acceleration kinematic equations (and sometimes they are very helpful) but often the textbooks present these as the main three to use.

 

[student 1]

Alright, so the velocity of both balls due to the squared velocities= Simply the same thing because acceleration and the distance they are from where the object was thrown are the same for both balls.