Help with this 9th grade motion problem

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SUMMARY

The discussion centers on a 9th-grade physics problem involving two stones thrown vertically upwards with initial velocities U1 and U2. The objective is to prove that the heights reached by the stones are in the ratio of U1 squared to U2 squared. Participants clarify that the formula S = u + at is not applicable for calculating height; instead, the correct approach involves using the conservation of energy principle, which relates the initial velocities to the maximum heights achieved.

PREREQUISITES
  • Understanding of kinematic equations for motion under constant acceleration
  • Familiarity with the concept of initial velocity in projectile motion
  • Basic knowledge of the law of conservation of energy
  • Ability to manipulate algebraic expressions and ratios
NEXT STEPS
  • Study the kinematic equation for height: S = ut + (1/2)at²
  • Learn about the law of conservation of energy in the context of projectile motion
  • Explore the derivation of height ratios in projectile motion problems
  • Practice solving similar problems involving multiple objects in motion
USEFUL FOR

Students studying physics, particularly those in 9th grade, educators teaching motion concepts, and anyone seeking to understand the principles of projectile motion and energy conservation.

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Help with this 9th grade "motion" problem

Homework Statement



2 stones are thrown vertically upwards with initial velocities U1 & U2. Prove that heights recahed by them is in ration U1squared:U2squared.

Homework Equations



S=u+at u being initial velocity

The Attempt at a Solution



since a and t will cancel out, ration should be u1: u2 not the squared. What am I missing?
 
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Use the conservation of energy to find the relationship between the 2 heights.
 


Care to explain it a bit more? Which is the equation you are referring to?

We are yet to learn law of conservation of energy.
 


If you throw a stone up with velocity U1, how high does it get?
 


johsun123 said:

Homework Statement



2 stones are thrown vertically upwards with initial velocities U1 & U2. Prove that heights recahed by them is in ration U1squared:U2squared.

Homework Equations



S=u+at u being initial velocity
This is incorrect. u+ at is the formula for the speed at t seconds given initial velocity u and acceleration t. Do you have a formula for distance or height of an object moving with constant acceleration?

The Attempt at a Solution



since a and t will cancel out, ration should be u1: u2 not the squared. What am I missing?
 

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