Juggler Problem, free falling.

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In summary, a juggler performs in a room with a ceiling height of 4.2 m above the level of his hands. He throws a ball vertically upward with an initial velocity of u, and it reaches the ceiling in a time of t. He then throws a second ball with the same initial velocity at the instant the first ball is at the ceiling. The two balls pass each other after a time of t, and when they pass, they are both at a height of 4.2 m above the juggler's hand. The equations that can be used to solve for the unknown variables are v=u+at, s=ut+1/2at^2, and v^2=u^2+2as.
  • #1
violin857
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A juggler performs in a room whose ceiling is 4.2 m above the leve of this hands. He throws a ball vertically upward so that it just reaches the ceiling.
a. with what initial velocity does he throw the ball?
b. what time is required for the ball to reach the ceiling.

He throws a second ball upward with the same initial velocity at the instant the first ball is at the ceiling.
c. how long after the second ball is thrown do the two balls pass each other?
d. when the balls pass each other, how far are they above the juggler's hand?
i understand how to do the equations and everything, i just don't know which apply with which? if someone could help me out be telling me which equations i would use, that would be great :)
 
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  • #2
best way to do this is to write out what you have:

s=4.2
u=?
v=0
a=-9.8
t=?

for Q1, you need to find u

the three equations you have are:

a) v=u+at
b) s=ut +1/2 a t^2
c) v^2=u^2 + 2as

you can't use a) or b) as you don't yet know t

so i'd say c) would work

do the same for your other questions i guess...
 

Related to Juggler Problem, free falling.

1. What is the "Juggler Problem"?

The "Juggler Problem" is a mathematical problem that involves calculating the trajectory of a juggler's hands while juggling objects that are falling freely due to gravity.

2. What factors affect the trajectory of the objects in the "Juggler Problem"?

The main factor that affects the trajectory of the objects is gravity. Other factors that may affect the trajectory include air resistance, the shape and weight of the objects, and the juggler's hand movements.

3. How is the "Juggler Problem" solved?

The "Juggler Problem" is typically solved using mathematical equations and principles of physics, such as Newton's laws of motion and the equations of motion for free-falling objects. Computer simulations may also be used to solve the problem.

4. What are some real-world applications of the "Juggler Problem"?

The "Juggler Problem" has applications in fields such as sports science, robotics, and entertainment. It can also be used to study the mechanics of juggling and improve juggling techniques.

5. Are there any limitations to the "Juggler Problem"?

One limitation of the "Juggler Problem" is that it assumes the objects are falling in a vacuum, without any air resistance. In reality, air resistance can significantly affect the trajectory of the objects. Other limitations may include the simplifications made in the mathematical models used to solve the problem.

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