What Is the Acceleration Needed to Stop an Arrow?

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Homework Help Overview

The problem involves an arrow shot vertically upward with an initial speed of 220 ft/s, which embeds itself 8 inches into the ground upon landing. The objective is to determine the constant acceleration required to stop the arrow.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the implications of assuming constant acceleration throughout the entire motion, questioning the validity of this assumption once the arrow strikes the ground. Some suggest focusing on the motion from the moment of impact to when the arrow stops.

Discussion Status

There is an ongoing exploration of the problem's assumptions, particularly regarding the use of constant acceleration. Some participants have offered alternative perspectives on the velocities involved, indicating a shift in how the problem might be approached.

Contextual Notes

Participants note the complexity introduced by changing acceleration once the arrow is embedded in the ground, highlighting the need for careful consideration of the motion's phases.

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Homework Statement


An arrow is shot straight up in the air with an initial speed of 220 ft/s. If on striking the ground it embeds itself 8.00 in into the ground, find the magnitude of the acceleration (assumed constant) required to stop the arrow, in units of feet/second^2.

Homework Equations


4 basic kinematic equations.

The Attempt at a Solution


Does anyone see where I went wrong in my work?
 

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The problem is just that you're using constant acceleration over the entire distance from the top of its path down to when it's embedded in the ground, which you can't do since the acceleration changes once it's in the ground. There's some funky stuff in your equations for plugging in the initial and final velocities because of this. Try instead using the interval from when the arrow hits the ground to when it stops 8 in. later.
 
Becomes a really easy problem when you know Vf=-Vi for velocities.
 
or in other words.. if you throw something up in the air with velocity V it will hit the ground at the same velocity V. So you can forget that part of the problem and pretend the arrow was just fired at the ground.
 

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