Short Webpage Title: Ball Toss Free Fall Equations

In summary, the time interval between when the first ball strikes the ground and the second ball strikes the ground is 0.5gt^2. The velocity of each ball as it strikes the ground is Vi.
  • #1
Ab17
99
2

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
 
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  • #2
Ab17 said:
Xf1 = h - vit - 0.5gt^2
OK.

Ab17 said:
Xf2 = vit - 0.5gt^2
Careful: They are both on the balcony.

Ab17 said:
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.
 
  • #3
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
 
  • #4
Ab17 said:
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.)
 
  • #5
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
 
  • #6
Ab17 said:
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.
 

1. What is free fall of ball toss?

Free fall of ball toss is a physical phenomenon where an object, in this case a ball, is dropped and falls towards the ground under the influence of gravity.

2. What factors affect the free fall of a ball toss?

The main factor that affects the free fall of a ball toss is the force of gravity. Other factors that may affect it include air resistance, the mass and size of the ball, and the height from which it is dropped.

3. How is the acceleration of a ball in free fall calculated?

The acceleration of a ball in free fall is calculated using the formula a = g, where "a" stands for acceleration and "g" is the acceleration due to gravity, which is approximately 9.8 m/s^2.

4. Does the mass of the ball affect its free fall?

Yes, the mass of the ball does affect its free fall. Objects with a greater mass experience a greater force of gravity, resulting in a faster acceleration towards the ground.

5. What is the difference between free fall and projectile motion?

The main difference between free fall and projectile motion is that in free fall, an object is only under the influence of gravity and falls straight down, while in projectile motion, an object is also moving horizontally and follows a curved path due to the influence of both gravity and its initial velocity.

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