Help Freefalling object problem

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SUMMARY

The problem involves calculating the height from which a freely falling object descends, given that it takes 1.60 seconds to travel the last 23.5 meters before impact. The relevant equations include kinematic equations for uniformly accelerated motion: \( v = u + gt \), \( s = ut + \frac{1}{2} gt^2 \), and \( v^2 = u^2 + 2gs \). The initial velocity (u) is 0, and the final velocity (v) at the end of the last 23.5 meters can be determined using these equations. By solving for the initial velocity of the last segment and using it as the final velocity for the first segment, the total height can be accurately calculated.

PREREQUISITES
  • Understanding of kinematic equations for uniformly accelerated motion
  • Basic knowledge of gravitational acceleration (g = 9.81 m/s²)
  • Ability to manipulate algebraic equations
  • Familiarity with the concept of free fall and initial/final velocities
NEXT STEPS
  • Review kinematic equations for free-fall motion
  • Practice solving problems involving gravitational acceleration
  • Explore the concept of initial and final velocities in motion equations
  • Learn about the derivation of kinematic equations from basic principles
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Students studying physics, particularly those focusing on mechanics and motion, as well as educators looking for examples of free-fall problems and their solutions.

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Homework Statement


A certain freely falling object requires 1.60 s to travel the last 23.5 m before it hits the ground. From what height above the ground did it fall?

Homework Equations


This is my last question on my online homework. Help! I have gotten answers, but the computer says they wrong.

The Attempt at a Solution


I know I have to set up two different equations, one for the last 23.5 m and one from the point that it fell at to the last 23.5m. I know the initial Velocity of the object is 0, and the final velocity of the initial drop is the initial velocity of the last 23.5m. Please help! I have tried it numerous times. My homework is due in 4 hours... Thanks :)
 
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You know the equations for a faling object.
v = u + gt
s = ut + 1/2 gt^2
v^2 = u^2 + 2gs

(s=distance, u=initial velocity, v=final velocity)
So you can work out the initial velocity ofthe last stage, and then use that as the final velocity of the first stage.
 

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