How long will it take for the baseball to reach John again if he misses it?

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Homework Help Overview

The problem involves a baseball thrown upwards by Rob at a speed of 14.2 m/s, with John positioned 4.5m above Rob in a tree. The discussion focuses on determining the time it takes for the baseball to reach John and the subsequent time it would take for the baseball to return to John if he misses it.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of the quadratic equation to find the time for the baseball to reach John and express confusion regarding the calculation for the time it takes for the baseball to return after being missed. Questions arise about the nature of the solutions obtained from the quadratic equation and the implications of negative roots.

Discussion Status

Some participants have provided insights into the quadratic solutions, noting that two roots are typically obtained, with one being negative and thus not applicable in this context. There is an ongoing exploration of potential errors in the setup or calculation, with requests for further clarification on the steps taken in solving the equation.

Contextual Notes

Participants are working under the constraints of the problem statement and are questioning the assumptions made regarding the motion of the baseball and the application of the quadratic formula. There is an emphasis on ensuring the correct signs are used in the equations.

khzak1
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Homework Statement


[/B]
1. Rob throws a baseball upwards at 14.2 m/s. His friend, John, is sitting in a tree 4.5m above Rob.

a. Calculate how long it will take to reach John.

b. If John misses the ball as it moves upwards, how long will it take to reach John again.

Homework Equations


Δd=V(Δt) + 1/2 (a)(Δt)^2

The Attempt at a Solution


I have found the time using the quadratic equation for part a which is 0.36s, but I am stuck on part b. I do not understand how to do it. It seems like Δd is the same in both parts. How in hell do I find Δt for part b.
 
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khzak1 said:

Homework Statement


[/B]
1. Rob throws a baseball upwards at 14.2 m/s. His friend, John, is sitting in a tree 4.5m above Rob.

a. Calculate how long it will take to reach John.

b. If John misses the ball as it moves upwards, how long will it take to reach John again.

Homework Equations


Δd=V(Δt) + 1/2 (a)(Δt)^2

The Attempt at a Solution


I have found the time using the quadratic equation for part a which is 0.36s, but I am stuck on part b. I do not understand how to do it. It seems like Δd is the same in both parts. How in hell do I find Δt for part b.
When you solve a quadratic, how many solutions do you get?
 
Well, you get 2 roots, but one is deemed useless because it is a negative.
 
khzak1 said:
Well, you get 2 roots, but one is deemed useless because it is a negative.

If you set up your equation correctly you'll get two positive roots, one being the 0.36 s you've found, and another at some later time.
Show your working and we'll see what went wrong.
 
-14.2 ± √113.35
-9.81

Δt=0.36s
Δt=-2.53s​
 
Your quadratic equation is correct, you've made an error somewhere while solving it.
 
khzak1 said:
-14.2 ± √113.35
-9.81

Δt=0.36s
Δt=-2.53s​
I'm guessing you made a sign error. Initial velocity is positive but acceleration is negative, so your -14.2 is the wrong sign. If you cannot spot your error, please post all steps.
 

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