Solving the Unequal Displacement of Balls Problem

In summary, the conversation is about finding a formula for the height of two balls that are thrown at different times and determining when they will be at the same height. One person asks for help with the question and the other person suggests finding formulas for the height of each ball and using them to determine the time when they are at the same height. The first person then thanks the other for their help and says they have figured it out.
  • #1
Lilly
12
0
hi, if anyone knows how to do this question, could you please get me started?

A ball is thrown upward from the ground with an initial speed of 23.2 m/s; at the same instant, a ball is dropped from a building 16.1 m high. After how long will the balls be at the same height?
thanks...
 
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  • #2
Find a formula for the height of the first ball as a function of time. call this h_1(t).

Find a formula for the height of the second ball; call that h_2(t).

Then what can you do with the two height formulas to find out when the two balls are at the same height?
 
  • #3
thanks, i figured it out! :)
 
  • #4
you're welcome. :smile:
 

What is the "Unequal Displacement of Balls Problem"?

The "Unequal Displacement of Balls Problem" is a physics problem that involves two balls of different masses being released from the same height at the same time, but with one ball having a horizontal velocity. The goal is to determine at what point the balls will collide, taking into account the effects of gravity and the different masses of the balls.

Why is this problem important?

This problem is important because it helps us understand the principles of motion and forces, specifically the effects of gravity and mass on an object's trajectory. It also has real-world applications, such as in sports where objects of different masses are in motion.

What factors affect the solution to this problem?

The solution to this problem is affected by several factors, including the initial horizontal velocity of the ball, the masses of the balls, the acceleration due to gravity, and the distance between the release points of the balls.

What are the steps to solving this problem?

The steps to solving this problem are as follows:
1. Identify the known values, such as the masses of the balls, the initial horizontal velocity, and the height of release.
2. Set up the equations of motion for each ball, taking into account the different masses and the acceleration due to gravity.
3. Use algebra to solve for the time at which the balls will collide.
4. Plug in the time value into the equations to determine the position of the balls at the point of collision.
5. Check the solution by making sure the position and time values are physically realistic.

What are some common mistakes when solving this problem?

Some common mistakes when solving this problem include not taking into account the different masses of the balls, not properly setting up the equations of motion, and making arithmetic errors. It is also important to remember to use consistent units throughout the problem, such as meters for distance and seconds for time.

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