Help with this 9th grade motion problem

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Two stones are thrown vertically upwards with initial velocities U1 and U2, and the task is to prove that the heights reached are in the ratio U1 squared to U2 squared. The initial attempt incorrectly suggests that the ratio of heights should be U1 to U2, as acceleration and time would cancel out. However, the correct approach involves using the kinematic equation for height, which relates initial velocity to the maximum height reached under constant acceleration. The discussion highlights the need for a proper formula for distance or height and clarifies that the conservation of energy principle has not yet been covered in their studies. Understanding the correct relationship between initial velocity and height is crucial for solving the problem accurately.
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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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