Short Webpage Title: Ball Toss Free Fall Equations

[Ab17]

Homework Statement

Two students are on a balcony a distance h above the S street. One student throws a ball vertically downward at a speed vi ; at the same time, the other student throws a ball vertically upward at the same speed. Answer the following symbolically in terms of vi, g, h, and t. (a) What is the time interval between when the first ball strikes the ground and the second ball strikes the ground? (b) Find the velocity of each ball as it strikes the ground. (c) How far apart are the balls at a time t after they are thrown and before they strike ground?

Homework Equations

Xf=xi + vt + 0.5at^2

3. Attempt solution

(a) Xf1 = h - vit - 0.5gt^2
Xf2 = vit - 0.5gt^2

0= h - Vit -0.5gt^2 (strike ground)
0 = Vit -0.5gt^2 (strike ground)

Therefore: Vit -05gt^2 = h - Vit - 0.5gt^2
t = h/2vi

Dont know what to do for (b) and (c) and not sure if the solution for (a) is even right

 

[Doc Al]

Xf1 = h - vit - 0.5gt^2

OK.

Xf2 = vit - 0.5gt^2

Careful: They are both on the balcony.

Therefore: Vit -05gt^2 = h - Vit - 0.5gt^2
t = h/2vi

Careful: The times are different! The t on the left is not the same as the t on the right.

Hint: Solve each one separately for the time it takes to hit the ground.

 

[Ab17]

Thank you I didnt realize both are on the balcony. So I should be using the time found in part a for part b and c

 

[Doc Al]

So I should be using the time found in part a for part b and c

Part a asks for the time difference, so you won't need that in the other parts. You'll need the same equations you used in part a to solve part c. For part b I would use a different kinematic equation altogether. (See if you can find one that meets your needs.)

 

[Ab17]

Is this right?

Xf1 = h + Vi.t - 0.5gt^2
Xf2 = h - Vi.t -0.5gt^2

0 = h + Vi.t - 0.5gt^2
0 = h - Vi.t -0.5gt^2

t1 = -2h /2vi - gt
t2 = 2h / 2vi + gt

t2-t1 = 8hvi/ 4vi^2 - g^2t^2

 

[haruspex]

t1 = -2h /2vi - gt
t2 = 2h / 2vi + gt

The t on the right is different in the two equations. The first is t1, the second t2.
I have no idea how you got the line after that.
Go back to the preceding pair of equations, the ones starting 0=h. Write them out properly, i.e. using t1 and t2 as appropriate.
There is quite a quick route from there, but if you can't spot it just solve those quadratic equations in the obvious way.