Discrepancy with Toricellis equation in a 2D kinematics prob

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SUMMARY

The discussion centers on a kinematics problem involving a stone thrown from a height of 2.1 meters at a 45-degree angle, with an initial velocity of 19.81 m/s. The calculated maximum height was found to be 10 meters from the starting position and 12.1 meters from the ground. The error arose when using the equation Vfin² = V0² + 2gΔy without considering the y-components of velocity, leading to an incorrect result of 20 meters. The correct approach requires focusing on the vertical components of motion to achieve accurate calculations.

PREREQUISITES
  • Understanding of 2D kinematics equations
  • Knowledge of projectile motion principles
  • Familiarity with vector components, specifically y-components of velocity
  • Basic grasp of gravitational acceleration (g = 9.81 m/s²)
NEXT STEPS
  • Review the derivation and application of 2D kinematics equations
  • Study the concept of vector decomposition in projectile motion
  • Practice solving projectile motion problems with varying angles and heights
  • Learn about the effects of air resistance on projectile trajectories
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and projectile motion, as well as educators seeking to clarify common misconceptions in these topics.

CherryWine
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Homework Statement


A stone is thrown from a height 2.1m with an angle of 45 degrees. It fell to the ground 42 m from the throwing position, measured horizontally. Initial velocity is 19,81 m/s, flight time is 3s what is the maximum height?

Homework Equations


All 2D kinematics equations.

The Attempt at a Solution


I plugged in the variables into the equation y(t), and equated Vfin=0, for the maximum height and obtained the correct result which should be 10m from the starting position and 12,1m from the ground. But when I tried to solve the problem using equation Vfin^2=V0^2+2gΔy I obtain 20m which is not correct. Why is it not correct?
 
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CherryWine said:
But when I tried to solve the problem using equation Vfin^2=V0^2+2gΔy I obtain 20m which is not correct. Why is it not correct?

You will need to show more of your work in order for us to find the error. Are the velocities in this equation supposed to be y-components of velocity?
 
TSny said:
You will need to show more of your work in order for us to find the error. Are the velocities in this equation supposed to be y-components of velocity?

Thank you very much! It was my careless mistake. I didn't use y-components of velocity. Thank you! Turns out to be consistent. Thanks again.
 

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