Kinetic Energy and Time Problem

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Homework Help Overview

The problem involves a ball projected horizontally from a table, initially possessing kinetic energy K, and later having kinetic energy 3K after a time t. The context is within the study of kinetic energy and projectile motion, specifically examining the relationship between time and kinetic energy while neglecting air resistance.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the equations relevant to projectile motion and question how to relate time to changes in kinetic energy. There is an exploration of whether the final velocity increases and how energy conservation principles apply.

Discussion Status

The discussion is ongoing, with participants offering different equations and concepts related to projectile motion. Some guidance has been provided regarding the conservation of energy, suggesting a need to consider potential energy loss in relation to the kinetic energy gain.

Contextual Notes

Participants are navigating the implications of neglecting air resistance and the assumptions regarding the initial conditions of the projectile's motion.

jtim36
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Homework Statement


A ball with mass m projected horizontally o the end of a table with an initial kinetic energy K. At a time t after it leaves the end of the table it has kinetic energy 3K. What is t? Neglect air resistance.
(answer: (2/g)(√K/m)

Homework Equations


E = 1/2 mv^2


The Attempt at a Solution


I understand what the problem is asking, but I don't get how to relate time and kinetic energy
 
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What equations do you know for the motion of a projectile under gravity?
 
x = vo(t) + 1/2at^2
v^2 = v0^2 + 2ah

Okay, so does that mean the final velocity was tripled then? and I apply the above equations?
 
jtim36 said:
x = vo(t) + 1/2at^2
v^2 = v0^2 + 2ah

Okay, so does that mean the final velocity was tripled then? and I apply the above equations?

No. Not tripled. Think conservation of energy. You have to gain energy 2K by losing potential energy mgh. Put time into it by figuring how long it takes to fall a distance h with zero initial vertical velocity.
 

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