Solve 1D Relative Motion Homework: Ball Thrown, Elevator, Tennis & Baseballs

In summary, the problem involves two balls meeting at the same point with the same speed. The first ball is dropped from the top of a building and after 2.00 seconds, the second ball is thrown upward from the ground. The speed of the upward-bound ball can be calculated using the equations vf2-v02=2a*Δx and x12=1/2*a12t^2 + v0,12t + x0, 12. The relative velocity of the two balls when they meet can be found using the equation vf = v0 + at.
  • #1
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Homework Statement



1)A ball is dropped from the top of a 56.0 m-tall building. After 2.00 s, another ball is thrown upward from the ground. When the two balls pass the same point, they have the same speed. How fast was the upward-bound ball thrown?

2)You are riding an elevator with an open roof. You are moving down at a speed of 4.00 m/s when you throw an apple up into the air at a speed of 6.00 m/s relative to the elevator.
a) How long does it take you to catch the apple?

3)A child has a tennis ball and a baseball. He let's go of the tennis ball from the top of a high building, waits , and then throws the baseball straight down with a speed such that the two balls have a relative speed of 10 m/s when they meet 40 m below. How long did the child wait before throwing the baseball?

4) You throw a ball up in the air with a speed such that it reaches your friend on a balcony 30.0 m above. At the same time, your friend throws another ball down to you such that it reaches you with twice the speed with which you threw your ball. What is the relative velocity of the two balls when they pass each other?

Answers:
1)33.1 m/s
2)a)1.77s
3)??
4)37 m/s

Homework Equations



vf2-v02=2a*Δx

x12=1/2*a12t^2 + v0,12t + x0, 12

vf = v0 + at



The Attempt at a Solution



I spent a lot of time trying all of these, my attempts are in a notebook

Basically, I just have trouble modelling the relationship, if you set up the equation with like 1 line of explanation I will likely be able to follow it

Thanks to anyone who helps me with 1/more problems
 
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  • #2
Let's take problem #1.

The balls meet at some time t. They meet at displacement x (let's place the origin at the ground). The ball going down has velocity -v, the ball going up has velocity v.

Write the equations relating t, v and x for both balls.
 
  • #3
ok, so what i did first is write the velocity and position for the dropped ball 2.00 seconds into its' "flight":

vf = -19.62 m/s (i choose up to be positive here)
xf = 36.4 m (above origin)

so now i guess they're in the"state" where they can be related using a relative equation

x12 = 0 + 0 + x

??
this is where i am confused. relative acceleration is zero so therefore the relative speed should always be constant?
 
  • #4
Why do you care where the dropped ball is in 2 seconds and what its velocity is? You are given the condition for its location and displacement at some later time t. It is unknown, so you end up having two equations for the dropped ball. Likewise, you will have equations for the other ball. Write them down.
 
  • #5
What would the distance they meet be?
 

1. What is 1D relative motion?

1D relative motion is the study of the motion of objects in one dimension (usually a straight line) relative to each other. It involves analyzing the velocities and positions of objects as they move in relation to each other.

2. How do you solve problems involving 1D relative motion?

To solve problems involving 1D relative motion, you must first identify the initial positions and velocities of all objects, as well as the time frame in which they are moving. Then, you can use equations such as the displacement equation and the relative velocity equation to determine the final positions and velocities of the objects.

3. How does throwing a ball in an elevator affect its motion?

Throwing a ball in an elevator affects its motion by changing its velocity and acceleration. As the elevator moves, it exerts a force on the ball which causes it to accelerate in the direction of the elevator's motion. This can result in the ball following a curved path rather than simply falling straight down.

4. How are 1D relative motion problems different in tennis and baseball?

In tennis, players are constantly changing their position on the court, which means their relative motion to the ball is constantly changing. This adds an extra level of complexity to solving 1D relative motion problems. In baseball, the motion of the ball is affected by factors such as air resistance and spin, which must be taken into account when solving 1D relative motion problems.

5. Can 1D relative motion be applied to real-world situations?

Yes, 1D relative motion is a fundamental concept in physics that can be applied to many real-world situations. For example, it can be used to analyze the motion of vehicles on a highway, the movement of objects in a roller coaster, or the flight of a ball in a sports game. Understanding 1D relative motion can help scientists and engineers design and optimize various systems and technologies.

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